7.6 Linear Programming Homework Name:_____________________________________________________________________________________________Period:____________ 1. A carpenter makes two types of bookcases. A large bookcase takes 6 hours to complete and a small bookcase takes 3 hours to complete. He can only spend 30 hours a week building bookcases. He must make at least 2 of each every week. If he earns a $50 profit on a large bookcase and a $20 profit on a small bookcase, how many of each must he make in order to maximize profit? What is the maximum profit?

2. A manufacturer produces two models of mountain bicycles. Model A requires 5 hours to assemble and 2 hours to paint. Model B requires 4 hours to assemble and 3 hours to paint. The maximum total weekly hours available are 200 hours in the assembly department and 108 hours in the painting department. The profits per unit are $25 for model A and $15 for model B. How many of each type should be produced to maximize profit? What is the maximum profit?

3. Rhonda is a farmer who grows barley and corn. Barley costs $60 per acre to plant and corn costs her $120 per acre to plant. She has $8,400 to spend and can plant at most 100 acres. How many acres of each should she plant to maximize her income if she earns $120 per acre on barley and $225 per acre on corn?