Linear Programming Practice Problems

The following problems can be found worked out at:  http://www.purplemath.com/modules/linprog3.htm

1)  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?

 

2)  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 model should you buy, in order to maximize storage volume?

 

3)  In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protien. But the rabbits should be fed no more than five ounces of food a day.

Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce.

What is the optimal blend?

 

The following problems can be found worked out at:  https://www.algebra.com/algebra/homework/coordinate/word/THEO-2012-01-26.lesson

4)  Fred's Coffee sells two blends of beans: Yusip Blend and Exotic Blend. Yusip Blend is one-half Costa Rican beans and one-half Ethiopian beans. Exotic Blend is one-quarter Costa Rican beans and three-quarters Ethiopian beans. Profit on the Yusip Blend is $3.50 per pound, while profit on the Exotic Blend is $4.00 per pound. Each day Fred receives a shipment of 200 pounds of Costa Rican beans and 330 pounds of Ethiopian beans to use for the two blends. How many pounds of each blend should be prepared each day to maximize profit? What is the maximum profit?

5)  The Mapple store sells Mapple computers and printers. The computers are shipped in 12-cubic-foot boxes and printers in 8-cubic-foot boxes. The Mapple store estimates that at least 30 computers can be sold each month and that the number of computers sold will be at least 50% more than the number of printers. The computers cost the store $1000 each and are sold for a profit of $1000. The printers cost $300 each and are sold for a profit of $350. The store has a storeroom that can hold 1000 cubic feet and can spend $70,000 each month on computers and printers. How man computers and how many printers should be sold each month to maximize profit? What is the maximum profit?

6)  The Appliance Barn has 2400 cubic feet of storage space for refrigerators. Large refrigerators come in 60-cubic-foot packing crates and small refrigerators come in 40-cubic-foot crates. Large refrigerators can be sold for a $250 profit and the smaller ones can be sold for $150 profit. How many of each type of refrigerator should be sold to maximize profit and what is the maximum profit if:
a) At least 50 refrigerators must be sold each month.
b) At least 40 refrigerators must be sold each month.
c) There are no restrictions on what must be sold.

7)  Shannon's Chocolates produces semisweet chocolate chips and milk chocolate chips at its plants in Wichita, KS and Moore, OK. The Wichita plant produces 3000 pounds of semisweet chips and 2000 pounds of milk chocolate chips each day at a cost of $1000, while the Moore plant produces 1000 pounds of semisweet chips and 6000 pounds of milk chocolate chips each day at a cost of $1500. Shannon has an order from Food Box Supermarkets for at least 30,000 pounds of semisweet chips and 60,000 pounds of milk chocolate chips. How should Shannon schedule its production so that it can fill the order at minimum cost? What is the minimum cost?

 

The following problems can be found worked out at:  http://www.ms.uky.edu/~rwalker/Class%20Work%20Solutions/Class%20work%207%20solutions.pdf

8)  A farmer is going to plant apples and bananas this year. It costs $ 40 per acre to plant apples and $ 60 per acre to plant bananas and the farmer has a maximum of $ 7400 available for planting. To plant apples trees requires 20 labor hours per acre; to plant banana trees requires 25 labor hours. Suppose the farmer has a total of 3300 labor hours available. If he expects to make a pro¯t of $ 150 per acre on apples and $ 200 per acre on bananas, how many acres each of apples and bananas should he cultivate?