Linear Programming
1) Bookcase Baffle
A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a large bookcase and 2 hours to make a small one. The carpenter can work no more than 32 hours a week on building bookcases and has to make at least 2 large and at least 2 small bookcases. The profit on a large bookcase is $35 and on a small one is $20. How many of each type of bookcase does the carpenter have to make to maximize his profit? What is his max profit?
2) Cookie Catastrophe
You are selling cookies for a bake sale. Your mom has 2 secret family recipes, chocolate chip and peanut butter cookies. You surveyed your friends and found that at least 8 of them want a batch of chocolate chip cookies and at least 12 of them want peanut butter cookies. However, because of time, you can only make at most 30 batches total. You can sell your chocolate chip cookies for 12$ and your peanut butter cookies for 15$. How many of each batch should you make to maximize your profit? What is your max profit?
3) Box Blunder
You are stenciling wooden boxes to sell at a fair. Stenciling takes 2 hours for a small box and 3 hours for a large box. You have no more than 30 hours available. You also have to make at least 3 small boxes. Profit for a small box is $10 and for a large is $20. How many of each size box should you sell you maximize your profit?
4) Rolesmill
The Rolesville Steel Mill can convert steel into girders and rods. The mill can produce at most 100 units of steel a day. At least 20 girders and at least 60 rods are required daily by regular customers. If the profit on a girder is $8 and the profit on a rod is $6, how many units of each types of steel should the mill produce each day to maximize their profit?
5) Car Cluster
The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space and a bus requires 30 square meters of space. The attendant can handle no more than 60 vehicles. If a car is charged $3.00 to park and a bus is charged $8.00, how many of each should the attendant accept to maximize income?
6) Farmer’s Fiasco
A farmer has a field of 70 acres in which he plants potatoes and corn. The seed for potatoes costs $30/acre, the seed for corn costs $60/acre and the farmer has set aside $3000 to spend on seed. The farmer wants to plant at least 10 acres of corn. The profit per acre of potatoes is $150 and the profit for corn is $50 an acre. Find the optimal solution for the farmer.
7) This is Nuts
A machine can produce either nuts or bolts, but not b0th at the same time. The machine can be used at most 8 hours a day. Furthermore at most 6 hours a day can be used for making nuts and at most 5 hours a day can be used for making bolts. There is a 2$ profit for each hour the machine is making nuts and a 3$ profit for each hour the machine is making bolts. How many hours per day should the machine make each item to maximize their profit? What is the max profit?