Introduction to Management Science, 10e (Taylor) Chapter 4 Linear Programming: Modeling Examples

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1 Introduction to Management Science, 10e (Taylor) Chapter 4 Linear Programming: Modeling Examples 1) When formulating a linear programming problem constraint, strict inequality signs (i.e., less than < or, greater than >) are not allowed. Diff: 2 Page Ref: Ch 2 review Key words: formulation 2) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the target cell. Diff: 2 Page Ref: Ch 2 review Key words: spreadsheet solution 3) The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign Diff: 2 Page Ref: Ch 2 review Key words: formulation, standard form 4) The standard form for the computer solution of a linear programming problem requires all variables to be on the left side, and all numerical values to be on the right side of the inequality or equality sign. Diff: 2 Page Ref: Ch 2 review Key words: formulation, standard form 5) Fractional relationships between variables are not permitted in the standard form of a linear program. Diff: 2 Page Ref: Ch 2 review Key words: formulation, standard form 1

2 6) A constraint for a linear programming problem can never have a zero as its right-hand-side value. Diff: 2 Page Ref: Ch 2 review Key words: formulation, standard form 7) The right hand side of constraints cannot be negative. Diff: 2 Page Ref: Ch 2 review Key words: formulation 8) A systematic approach to model formulation is to first define decision variables. Diff: 1 Page Ref: Ch 2 review Key words: formulation 9) A systematic approach to model formulation is to first construct the objective function before determining the decision variables. Diff: 1 Page Ref: Ch 2 review Key words: formulation 10) In a linear programming model, a resource constraint is a problem constraint with a greaterthan-or-equal-to ( ) sign. Diff: 1 Page Ref: Ch 2 review Key words: formulation 11) Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. Diff: 2 Page Ref: Main Heading: A Product Mix Example Key words: formulation, product mix problem 12) Product mix problems cannot have "greater than or equal to" ( ) constraints. Diff: 2 Page Ref: Main Heading: A Product Mix Example Key words: product mix 2

3 13) When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: objective function 14) When using a linear programming model to solve the "diet" problem, the objective is generally to maximize nutritional content. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: objective function 15) In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: formulation, diet example 16) Solutions to diet problems in linear programming are always realistic. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: diet example 17) Diet problems usually maximize nutritional value. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: diet example 18) In most media selection decisions, the objective of the decision maker is to minimize cost. Diff: 2 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 19) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the audience exposure. Diff: 2 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 3

4 20) Linear programming model of a media selection problem is used to determine the relative value of each advertising media. Diff: 3 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 21) In a media selection problem, maximization of audience exposure may not result in maximization of total profit. Diff: 2 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 22) In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities. Diff: 2 Page Ref: Key words: transportation problem, formulation 23) In an unbalanced transportation model, supply does not equal demand and supply constraints have signs. Diff: 2 Page Ref: Key words: transportation problem, formulation 24) Transportation problems can have solution values that are non-integer and must be rounded. Diff: 3 Page Ref: Key words: transportation problem, solution 25) In a transportation problem, the supply constraint represents the maximum amount of product available for shipment or distribution at a given source (plant, warehouse, mill). Diff: 1 Page Ref: Key words: transportation problem, formulation 4

5 26) In a transportation problem, a supply constraint (the maximum amount of product available for shipment or distribution at a given source) is a greater-than-or equal-to constraint ( ). Diff: 2 Page Ref: Key words: transportation problem, formulation 27) In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store). Diff: 2 Page Ref: Key words: transportation problem, formulation 28) In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint ( ). Diff: 2 Page Ref: Key words: transportation problem, formulation 29) Blending problems usually require algebraic manipulation in order to write the LP in "standard form." Diff: 1 Page Ref: Main Heading: Data Envelopment Analysis Key words: blending 30) Data Envelopment Analysis indicates which type of service unit makes the highest profit. Diff: 1 Page Ref: Key words: blending 31) Data Envelopment Analysis indicates the the relative of a service unit compared with others. Answer: efficiency or productivity Diff: 2 Page Ref: Main Heading: Data Envelopment Analysis Key words: data envelopment analysis 5

6 32) types of linear programming problems often result in fractional relations between variables which must be eliminated. Answer: blending Diff: 2 Page Ref: Key words: blending 33) When formulating a linear programming model on a spreadsheet, the measure of performance is located in the cell. Answer: target Diff: 2 Page Ref: 113 Key words: spreadsheet solution 34) When the command is used in an Excel spreadsheet, all the values in a column (or row) are multiplied by the values in another column (or row) and then summed. Answer: SUMPRODUCT Diff: 2 Page Ref: 117 Key words: spreadsheet solution 35) For product mix problems, the constraints are usually associated with. Answer: resources or time Diff: 2 Page Ref: Main Heading: A Product Mix Example Key words: product mix 36) The for the computer solution of a linear programming problem requires all variables on the left side, and all numerical values on the right side of the inequality or equality sign. Answer: standard form Diff: 2 Page Ref: Main Heading: A Product Mix Example Key words: formulation, constraint 37) The objective function of a diet problem is usually to subject to nutritional requirements. Answer: minimize costs Diff: 1 Page Ref: Main Heading: A Diet Example Key words: diet problem 6

7 38) Investment problems maximize. Answer: return on investments Diff: 1 Page Ref: Main Heading: An Investment Example Key words: investment 39) In a media selection problem, instead of having an objective of maximizing profit or minimizing cost, generally the objective is to maximize the. Answer: audience exposure Diff: 2 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 40) In problem, maximization of audience exposure may not result in maximization of total profit. Answer: media selection Diff: 3 Page Ref: Main Heading: Marketing Example Key words: marketing problem, media selection 41) In a balanced transportation model, supply equals. Answer: demand Diff: 2 Page Ref: Key words: transportation problem, formulation 42) In a transportation problem, supply exceeds demand. Answer: unbalanced Diff: 2 Page Ref: Key words: transportation problem, formulation The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $

8 43) What is the formulation for this problem? Answer: MAX Z = 0. 4L + 0.5V s.t. 2L + 3V L + 8V L + 2V 2000 Diff: 1 Page Ref: Main Heading: Product Mix Example Key words: computer solution 44) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining? Answer: salt only, 1400 ounces remaining Diff: 1 Page Ref: Main Heading: A Product Mix Example Key words: slack, computer solution 45) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining? Answer: salt only, 1400 ounces remaining Diff: 1 Page Ref: Main Heading: A Product Mix Example Key words: slack, computer solution A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond- filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. 46) This represents what type of linear programming application? Answer: product mix Diff: 1 Page Ref: Main Heading: Product Mix Example Key words: computer solution 8

9 47) What is the formulation for this problem? Answer: MAX Z = $.20B + $.30C s.t. 6B + 3C B + 1C B + 4C 4800 C 400 Diff: 1 Page Ref: Main Heading: Product Mix Example Key words: formulation, constraint 48) For the production combination of 600 bear claws and 800 almond filled croissants, how much flour and almond paste is remaining? Answer: flour = 0 ounces and almond paste = 0 ounces Diff: 1 Page Ref: Main Heading: A Product Mix Example Key words: slack, computer solution 49) If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company's 3 products in period 2 is equal to 400. Answer: X12 + X22 + X Diff: 2 Page Ref: Key words: transportation problem, supply constraint 9

10 50) Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility. Write the formulation for this problem. Answer: MIN Z = 4x1A + 4.5x1B + 3.2x1C + 3.5x2A + 3x2B +4x2C + 4x3A + 3.5x3B x3C s.t. x1a + x1b +x1c = 200 x2a + x2b +x2c = 200 x3a + x3b +x3c = 300 x1a + x2a +x3a = 250 x1b + x2b +x3b = 150 x1c + x2c +x3c = 200 Diff: 2 Page Ref: Key words: computer solution, transportation/distribution 51) Quickbrush Paint Company makes a profit of $2 per gallon on its oil-base paint and $3 per gallon on its water-base paint. Both paints contain two ingredients, A and B. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. The company wishes to use linear programming to determine the appropriate mix of oil-base and water-base paint to produce to maximize its total profit. How much oil based and water based paint should the Quickbrush make? Answer: 9167 gallons of water based paint and 5833 gallons of oil based paint Diff: 2 Page Ref: Key words: blending 10

11 Andy Tyre manages Tyre's Wheels, Inc. Andy has received an order for 1000 standard wheels and 1200 deluxe wheels next month, and for 750 standard wheels and 1000 deluxe wheels the following months. He must fill all the orders. The cost of regular time production for standard wheels is $25 and for deluxe wheels, $40. Overtime production costs 50% more. For each of the next two months there are 1000 hours of regular time production and 500 hours of overtime production available. A standard wheel requires.5 hours of production time and a deluxe wheel,.6 hours. The cost of carrying a wheel from one month to the next is $2. 52) Define the decision variables and objective function for this problem. Answer: Define the decision variables: S1R = number of standard wheels produced in month 1 on regular time production S1O = number of standard wheels produced in month 1 on overtime production S2R = number of standard wheels produced in month 2 on regular time production S2O = number of standard wheels produced in month 2 on overtime production D1R = number of deluxe wheels produced in month 1 on regular time production D1O = number of deluxe wheels produced in month 1 on overtime production D2R = number of deluxe wheels produced in month 2 on regular time production D2O = number of deluxe wheels produced in month 2 on overtime production Y1 = number of standard wheels stored from month 1 to month 2. Y2 = number of deluxe wheel s stored from month 1 to month 2. MIN 25 S1R S1O +40 D1R + 60 D1O + 25 S2R S2O +40 D2R + 60 D2O +2 Y1 +2 Y2 Diff: 2 Page Ref: Main Heading: Multiperiod Scheduling Key words: linear program multiperiod scheduling 53) Write the constraints for this problem. Answer: S1R + S1O - Y1 = S1R +.6 D1R 1000 D1R + D1O - Y2 = S1O +.6 D1O 500 S2R + S2O + Y1 = S2R +.6 D2R 1000 D2R + D2O + Y2 = S2O +.6 D12O 50 Diff: 2 Page Ref: Main Heading: Multiperiod Scheduling Key words: linear program multiperiod scheduling 11

12 Bullseye Shirt Company makes three types of shirts: Athletic, Varsity, and Surfer. The shirts are made from different combinations of cotton and rayon. The cost per yard of cotton is $5 and the cost for rayon is $7. Bullseye can receive up to 4,000 yards of cotton and 3,000 yards of rayon per week. The table below shows relevant manufacturing information: Minimum Shirt Total Yards of Fabric fabric per shirtrequirement weekly contracts Maximum Demand Selling Price at least 60% Athletic 1.00 cotton $30 Varsity 1.20 no more than 30% rayon $40 Surfer 0.90 As much as 80% cotton $36 54) Assume that the decision variables are defined as follows: A = total number of athletic shirts produced V = total number of varsity shirts produced S = total number of surfer shirts produced C = yards of cotton purchased R = yards of rayon purchased Xij = yards of fabric i (C or R) blended into shirt J (A, V or S) Write the objective function. Answer: max 30 A + 40 V + 36 S - 5C - 7R Diff: 2 Page Ref: Key words: objective function, model construction 55) Write the constraints for the fabric requirements. Answer: Form of constraints: Total yards used is greater than (or less than) total yards required x (% fabric required) shirts produced XCA 0.6 A XVR 0.36V XSC 0.72 S Diff: 2 Page Ref: Key words: blending 12

13 56) Write the constraints for the total number of shirts of each style produced. Answer: Form of constraint: number of shirts produced = (total yards used to make the shirt)/ (yards/shirt) A =( XCA + XRA)/1 V =( XCV + XRV)/1.2 S =( XCS + XRS)/0.9 Standard form: A -XCA - XRA) = V - XCV - XRV =0 0.9 S - XCS - XRS=0 Diff: 3 Page Ref: Key words: blending 57) Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel's cat food is made by mixing two types of cat food to obtain the "nutritionally balanced cat diet." The data for the two cat foods are as follows: Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the cost of this plan, and how much fat and protein do the cats receive? Answer: Cost is $3.50, which uses 16 cans of meow munch and 2 cans of feline fodder. Diff: 2 Page Ref: Main Heading: A Diet Example Key words: diet 13

14 58) A credit union wants to make investments in the following: The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: Risk free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total. Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans) Consumer loans plus other secured loans may not exceed the vehicle loans Other secured loans plus signature loans may not exceed the funds invested in risk free securities. How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return? Answer: Diff: 3 Page Ref: Main Heading: Investment Example Key words: investment 59) When systematically formulating a linear program, the first step is A) Construct the objective function B) Formulate the constraints C) Identify the decision variables D) Identify the parameter values E) Identify a feasible solution Answer: C Diff: 2 Page Ref: 112 Main Heading: Formulation Key words: formulation 14

15 60) The following types of constraints are ones that might be found in linear programming formulations: = 3. > A) 1 and 2 B) 2 and 3 C) 1 and 3 D) all of the above Answer: A Diff: 2 Page Ref: Review Main Heading: A Product Mix Example Key words: formulation, constraint 61) Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as: A) x2.60 B) x2.60 (x2 + x7 + x8) C).4x2 -.6x7 -.6x8 0 D).4x2 -.6x7 -.6x8 0 E) -.4x2 +.6x7 +.6x8 0 Answer: C Diff: 3 Page Ref: Main Heading: An Investment Example Key words: formulation 15

16 62) The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient. Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds) The constraint for ingredient 3 is: A).5A +.75B = 20 B).3B = 20 C).3 B 20 D).3B 20 E) A + B =.3(20) Answer: D Diff: 2 Page Ref: Main Heading: A Diet Example Key words: solution The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $ ) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which of the three resources is (are) not completely used? A) flour only B) salt only C) herbs only D) salt and flour E) salt and herbs Answer: B Diff: 2 Page Ref: Main Heading: Product Mix Example Key words: solution, slack 16

17 64) What is the constraint for salt? A) 6L + 8V 4800 B) 1L + 2V 4800 C) 3L + 2V 4800 D) 2L + 3V 4800 E) 2L + 1V 4800 Answer: D Diff: 2 Page Ref: Main Heading: Product Mix Example Key words: formulation, constraint 65) Which of the following is not a feasible production combination? A) 0L and 0V B) 0L and 1000V C) 1000L and 0V D) 0L and 1200V Answer: D Diff: 1 Page Ref: Main Heading: Product Mix Example Key words: formulation, feasibility 66) If Xab = the production of product a in period b, then to indicate that the limit on production of the company's "3" products in period 2 is 400, A) X B) X21 + X22 + X C) X12 + X22 + X D) X12 + X22 + X E) X Answer: C Diff: 2 Page Ref: Main Heading: Product Mix Example Key words: formulation, constraint 67) Balanced transportation problems have the following type of constraints: A) B) C) = D) < E) None of the above Answer: C Diff: 2 Page Ref: Key words: formulation, constraint 17

18 68) Compared to blending and product mix problems, transportation problems are unique because A) They maximize profit. B) The constraints are all equality constraints with no " " or " " constraints. C) They contain fewer variables. D) The solution values are always integers. E) All of the above are True. Answer: D Diff: 2 Page Ref: Key words: transportation 69) The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint? A) 2R + 4D 480 B) 2D + 4R 480 C) 2R + 3D 480 D) 3R + 2D 480 E) 3R + 4D 480 Answer: A Diff: 2 Page Ref: Key words: formulation, constraint 70) A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit? A) $380 B) $400 C) $420 D) $440 E) $480 Answer: A Diff: 2 Page Ref: Key words: computer solution 18

19 71) The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit? A) $220 B) $270 C) $320 D) $420 E) $520 Answer: D Diff: 2 Page Ref: Key words: computer solution 72) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1. A) x21 + x B) x12 + x C) x11 + x D) x21 + x E) x11 + x Answer: C Diff: 2 Page Ref: Key words: formulation 19

20 73) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the demand constraint for gasoline type 1. A) x21 + x22 = B) x12 + x22 = C) x11 + x D) x11 + x21 = E) x11 + x Answer: D Diff: 2 Page Ref: Key words: formulation 74) Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the constraint stating that the component 1 cannot account for more than 35% of the gasoline type 1. A) x11 + x12 (.35)(x11 + x21) B) x11.35 (x11 + x21) C) x11.35 (x11 + x12) D) -.65x x21 0 E).65x x21 0 Answer: E Diff: 3 Page Ref: Key words: formulation 20

21 75) Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil based and water based paint. The oil-base paint contains 90 percent A and 10 percent B, whereas the water-base paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil based paint, and y represents the gallons of water based paint, which constraint is correctly represents the constraint on ingredient A? A).9A +.1B 10,000 B).9x +.1y 10,000 C).3x +.7y 10,000 D).9x +.3y 10,000 E).1x +.9y 10,000 Answer: D Diff: 2 Page Ref: Key words: blend 76) A systematic approach to model formulation is to first A) construct the objective function B) develop each constraint separately C) define decision variables D) determine the right hand side of each constraint E) all of the above Answer: C Diff: 2 Page Ref: 112 Main Heading: A Multiperiod Scheduling Example Key words: model formulation 77) Let: rj = regular production quantity for period j, oj =overtime production quantity in period j, ii = inventory quantity in period j, and di = demand quantity in period j Correct formulation of the demand constraint for a multi-period scheduling problem is: A) rj + oj + i2 - i1 di B) rj + oj + i1 - i2 di C) rj + oj + i1 - i2 di D) rj - oj - i1 + i2 di E) rj + oj + i2 - i1 di Answer: A Diff: 2 Page Ref: Main Heading: A Multiperiod Scheduling Example Key words: formulation, constraint 21

22 78) In a multi-period scheduling problem the production constraint usually takes the form of: A) beginning inventory + demand - production = ending inventory B) beginning inventory - demand + production = ending inventory C) beginning inventory - ending inventory + demand = production D) beginning inventory - production - ending inventory = demand E) beginning inventory + demand + production = ending inventory Answer: B Diff: 2 Page Ref: Main Heading: A Multiperiod Scheduling Example Key words: model formulation, multi-period scheduling problem 79) The type of linear program that compares services to indicate which one is less productive or inefficient is called A) product mix B) data envelopment analysis C) marketing D) blending E) multi period scheduling Answer: B Diff: 2 Page Ref: 140 Main Heading: Data Envelopment Analysis Key words: formulation In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2, an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to $50,000 to invest. 80) The stockbroker suggests limiting the investments so that no more than $10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed 350, whichever is more restrictive. How would this be formulate as a linear programming constraint? A) X X2 + X3 350 B) 10,000 X2 350X X3 C) 47.25X2 10,000 X2 + X3 350 D) 47.25X2 10, X X3 350 Answer: C Diff: 2 Page Ref: Main Heading: An Investment Example Key words: investment 22

23 81) An appropriate part of the model would be A) 15X X X3 50,000 B) MAX 15X X X3 C) X1 + X2 +X3 50,000 D) MAX 50(15)X (47.25)X (110)X3 Answer: A Diff: 2 Page Ref: Main Heading: An Investment Example Key words: investment 82) The expected returns on investment of the three stocks are 6%, 8%, and 11%. An appropriate objective function is A) MAX.06X1 +.08X2 +.11X3 B) MAX.06(15)X1 +.08(47.25)X2 +.11(110)X3 C) MAX 15X X X3 D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3 Answer: B Diff: 2 Page Ref: Main Heading: An Investment Example Key words: investment 83) The investor stipulates that stock 1 must not account for more than 35% of the number of shares purchased. Which constraint is correct? A) X B) X1 = 0.35 (50000) C) X1 0.35(X1 + X2 +.X3) D) X1 = 0.35(X1 + X2 +.X3) Answer: C Diff: 2 Page Ref: Main Heading: An Investment Example Key words: investment 23