Check HW: WS Calculator Linear Programming

Transcription

1 Check HW: WS Calculator Linear Programming A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 profit, and each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

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3 Check HW: WS Calculator Linear Programming

4 Check HW Answers posted below: 3-4B WS 1. x = # acres of wheat y = # acres of rye 2. x = tons of ore from source A y = tons of ore from source B 3. x = # sheets of plywood y = # sheets of pressure treated 4. x = # TVs y = # DVD Players

5 Check HW Answers posted below: 3-4B WS 5. x = ounces of Food X y = ounced of Food Y 6. x = # of scientific calc y = # of graphing calc 7. x = # of cabinet X y = # of cabinet Y 8. x = $ in municipal bonds y = $ in CDs z = $ in high risk account

6 16 point CW & HW: Linear Programming WS 3-4C 1. An electronics company makes two kinds of TV s: LCD and plasma. Let x be the number of LCD TV s and y be the number of plasma TV s made in a month. The company has enough equipment to make as many as 1000 LCD TV s per month or 600 plasma TV s per month. It takes 20 worker-hours to make a LCD TV and 30 worker-hours to make a plasma TV. The company has up to 24,000 worker-hours of labor available each month. They make $75 profit on LCD TV s and $125 on plasma TV s. a) Write the objective function: b) Identify the variables and write the 5 constraints. You may set up a table: c) Graph the constraints for this system and label the vertices Help students set up their axes. e) Substitute vertices into objective function: f) What combination of LCD and plasma TV s will maximize profit? What will be the monthly profit?

7 2. A painter has exactly 32 units of yellow dye and 54 units of blue dye. He plans to mix as many gallons as possible of Light Green and Dark Green. Each gallon of Light Green requires 4 units of yellow and 1 unit of blue. Each gallon of Dark Green requires 1 unit of yellow and 6 units of blue. A gallon of Light Green generates a profit of $10 and a gallon of Dark generates a profit of $15. How many gallons of each color of green should the painter mix to maximize profits? a) Write the objective function: b) Identify the variables and write 4 constraints. You may set up a table: c) Graph the constraints for this system and label the vertices: e) Substitute vertices into objective function: f) How many gallons of each color of green should the painter mix to maximize profits? What will be the profit?

8 3. A landscaping contractor uses a combination of two brands of fertilizers, each containing different amounts of phosphates and nitrates, as shown in the table: Phosphate Content per Package Nitrate Content per Package Brand A Brand B Requirements 4 lbs 6 lbs 24 lbs 2 lbs 5 lbs 15 lbs A certain lawn requires a mixture of at least 24 lbs of phosphates and at least 15 lbs of nitrates. Let a = the number of packages of Brand A and b = the number of packages of Brand B. Now, if a package of Brand A costs $6.99 and a package of Brand B costs $17.99, how many packages of each would minimize the contractor s cost? a) Write an objective function: b) List 4 constraints: c) Graph the feasible region and identify the vertices. d) Substitute vertices into objective function: e) How many packages of each would minimize the contractor s cost? How much would it cost?

9 4. Suppose your mom is shopping for groceries. From a nutrition table she has learned that one ounce of hamburger has 1 mg of iron, 10 mg of Vitamin A, and 4 g of protein. One medium potato has 2 mg of iron, 0 mg of Vitamin A, and 3 g of protein. For dinner, your mom wants you to have at least 8 mg of iron, 30 mg of Vitamin A, and 27 g of protein to meet your daily nutritional requirements. If one medium potato costs $0.10 and one ounce of hamburger costs $0.15, how many potatoes and what number of ounces of hamburger should your mother buy to minimize the grocery bill? a) Write an objective function: b) Create a table to organize the given information. Hamburger Potatoes Requirements Iron Vitamin A Protein c) Write a system of 5 constraints using the information in the table. d) Graph the system of inequalities. Identify the vertices of the feasible region. e) Substitute vertices into objective function: f) How manypotatoes and what number of ouncesof hamburger should your mother buy to minimize the grocery bill? How much is the bill?