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1 Raising Money You and your classmates decide to sell sweatshirts and T-Shirts to raise money for a school trip. You decide that you should sell at least 30 items, but do not want to exceed 120 items. Based on a small survey of students, you also decide that the number of T-Shirts should be at least twice the number of sweatshirts. Assume the profit on each sweatshirt is $5 and the profit on each T-shirt is $2. What is the maximum profit you can obtain? The Snack Problem Assume you like snacks and insist on having at least one serving of dry roasted peanuts and one serving of potato chips each day. Each serving of the peanuts contains 15% of the recommended daily allowance of saturated fat; each serving of potato chips contains 10%. Each serving of the peanuts contains 12% of the recommended amount of dietary fiber; each serving of potato chips contains 5%. You determine that you want to consume no more than 60% of the recommended allowance of dietary fat from these two snacks, but you want to get at least 30% of the recommended allowance of fiber from them. The peanuts cost 12.4 cents per serving and the potato chips cost 23.2 cents per serving. If you keep within the constraints mentioned, how many servings of each should you have each day to minimize your cost. DogGoneIt Ross Kingley and Sara Tennis opened a pet store called DogGoneIt several years ago. Since opening in 2001, business has been very good with revenue increasing each year. To expand their business and increase their profit even more, Ross and Sara want to start selling T-Shirts and License plate frames with their store insignia on them. Because they are now successful entrepreneurs, they have done their research and plan to sell the T-Shirts and License plate frames with the following constraints. They will have in stock no more than 100 T-Shirts and Covers per day They will sell at least 10 and no more than 60 T-Shirts per day They will sell at least 20 License plate frames per day Further, given that they have a relative who already owns a business that designs logos, they determine that they will make a profit of $10 on each T-Shirt and $12 on each License plate frame. Determine how many T-Shirts and License Plate frames they must sell to maximize profit.

2 EatUp! Andrew and Jessica have opened a Health food store called EatUp! They sell different banana bread blends. The table below shows the amount of Nutrient A and Nutrient B in 2 types of banana bread, X and Y. Banana Bread Amount of Nutrient A Amount of Nutrient B X 1 unit per pound 1/2 unit per pound Y 1/3 unit per pound 1 unit per pound The BHS cross country team must eat at least 40 lbs of banana bread per day. The bread must be a mixture of type X and type Y. The daily diet must include at least 20 units of Nutrient A and at least 30 units of nutrient B. The girls must not get more than 100 pounds of banana bread per day. If Banana Bread X costs 80 cents per pound and Banana Bread Y costs 40 cents per pound. What is the least possible cost per day for feeding the girls. SuperSport Inc. The Oklahoma City division for SuperSport Inc. produces footballs and basketballs. It takes 4 hours on Machine A and 2 hours on Machine B to make a football. Producing a basketball requires 6 hours on Machine A, 6 hours on Machine B, and 1 hour on Machine C. Machine A is available 120 hours per week, Machine B is available 72 hours a week, and Machine C is available 10 hours per week. If the company makes $3 profit on each football and $2 profit on each basketball, how many of each should they make to maximize profit?

3 Cracker Company A company makes whole wheat crackers and sesame crackers. The crackers are sold by the box. Each box contains 5 packets of whole wheat crackers or 3 packets of sesame crackers. The company cannot produce more than 150 packets of crackers per minute, but at least 15 boxes of whole wheat crackers and at least 20 boxes of sesame crackers must be produced per minute. If the profit per box of whole wheat crackers is 10 cents and the profit per box of sesame crackers is 5 cents, how many boxes of each type should be produced per minute in order to maximize profits? Growing a Garden Kay grows and sells tomatoes and green beans. It costs $1 to grow a bushel of tomatoes, and it takes 1 square yard of land. It costs $3 to grow a bushel of beans, and it takes 6 square yards of land. Kay s budget is $15, and she has 24 square yards of land available. If she makes $1 profit on each bushel of tomatoes and $4 profit on each bushel of beans, how many bushels of each should she grow in order to maximize profit? Clock Work Juan makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 ounce of varnish. It also takes 2 hours to assemble an oak clock, which takes 4 ounces of varnish. Juan has 16 ounces of varnish in stock, and he can work 20 hours. If he makes $3 profit on each pine clock and $4 on each oak clock, how many of each type should he make to maximize his profit?

4 10K Race Brad is an organizer of a 10K race and must hire workers for a one day to prepare the race packets. Skilled workers cost $60 a day, and students cost $40 a day. Brad can spend no more than $1,440. He needs at least 1 skilled worker for every 3 students, but only 16 skilled workers are available. Skilled workers can prepare 25 packets per hour and students can prepare 18 packets per hour. Find the number of each type of worker that Brad should hire to maximize the number of packets produced. Filing Cabinets You need to buy some filing cabinets. You know that Cabinet X Costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don t have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which models should you buy, in order to maximize storage volume Calculators 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 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

5 Student Council Student Council is having a talent show. According to school policy, no more than 450 student tickets may be sold and no more than 250 general admission tickets may be sold. It costs $0.50 per ticket to advertise the show to the students and $1 per ticket to advertise the show to the general public. The advertising budget is $300 for this show. Student Council charges $5 for a student ticket and $8 for a general admission ticket. How many of each type of ticket should they sell to make the maximum profit? What is the maximum profit? Barley and Rye A farmer has 300 acres on which he can plant any combination of two crops, barley and rye. Barley requires 5 worker-days and $15 capital for each acre planted, while rye requires 2 workerdays and $20 capital for each acre planted. Suppose that barley yields $20 per acre and rye $30 per acre. The farmer has $4000 capital and 750 worker-days of labor available for the year. Determine the most profitable strategy. Econojet Airlines Econojet Airlines sells business class and tourist class seats for its charter flights. To charter a plane, at least 5 business class tickets must be sold and at least 9 tourist class tickets must be sold. The plane does not hold more than 30 passengers. Econojet makes $40 profit for each business class ticket sold and $45 profit for each tourist class ticket sold. In order for Econojet Airlines to maximize its profits, how many of each type of ticket should they sell? What is the maximum profit?