College Algebra – 10.8b – Linear Programming Name: ______
1. In a factory, machine 1 produces 8-inch pliers at a rate of 60 units per hour and 6-inch pliers at a rate of 70 units per hour. Machine 2 produces 8-inch pliers at a rate of 40 units per hour and 6-inch pliers at a rate of 20 units per hour. It costs $50 per hour to operate machine 1 and $30 per hour to operate machine 2. The production schedule requires that at least 240 units of 8-inch pliers and at least 140 units of 6-inch pliers be produced during each 10-hour day. What combination of machines will cost the least money to operate? What is this minimum cost?
2. A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for rear-projection and $200 for plasma televisions. Equipment in the factory is limited to making at most 450 rear-projection and 200 plasma televisions per month. The cost per unit is $600 for rear-projection and $900 for plasma televisions. The total monthly costs cannot exceed $360,000. How many televisions of each type should the manufacturer make to maximize their profit? What is the maximum profit?
3. You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you do to maximize your score? What is the maximum score?
4. An owner of a fruit orchard hires a crew of workers to prune at least 25 of his 50 fruit trees. Each newer tree requires one hour to prune, while each older tree needs one-and-a-half hours. The crew contracts to work for at least 30 hours and charge $15 for each newer tree and $20 for each older tree. To minimize the cost, how many of each kind of tree will the orchard owner have pruned? What will be the cost?
5. An entrepreneur is having a design group produce at least six samples of a new kind of zipper that he wants to market. It costs $9.00 to produce each metal zipper and $4.00 to produce each plastic zipper. He wants to have at least two of each version of the zipper and needs to have all the samples 24 hours from now. It takes 4 hours to produce each metal sample and 2 hours to produce each plastic sample. To minimize the cost of the samples how many of each kind should the entrepreneur order? What will be the cost of the samples?
6. A certain diet requires at most 60 units of carbohydrates, 45 units of protein, and 30 units of fat each day. Each ounce of Supplement A provides 5 units of carbohydrates, 3 units of protein, and 4 units of fat. Each ounce of Supplement B provides 2 units of carbohydrates, 2 units of protein, and 1 unit of fat. If Supplement A costs $1.50 per ounce and Supplement B costs $1.00 per ounce, how many ounces of each supplement should be taken daily to minimize the cost of the diet? What will the minimum cost be?
7. A manufacturer makes two types of jet skis, regular and deluxe. The profit on a regular jet ski is $200 and the profit on the deluxe model is $250. To meet customer demand, the company must manufacture at least 50 regular jet skis per week and at least 75 deluxe models. To maintain high quality, the total number of both models should not exceed 150 per week. How many jet skis of each type should be manufactured per week to maximize profit? What is the maximum weekly profit?