Linear Programming II

For each problem do the following:

A. Create a resource table B. Give the system of inequalities that describe this situation C. Graph the feasible region and label all corner points D. Maximize the profits

1. A manufacturer will create skateboards and dolls. He has 80 containers of plastic available and 360 person minutes to use. Each skate board requires 5 containers of plastic and will use 18 minutes of labor. Each doll will require 2 containers of plastic and will use 15 minutes of labor. Due to demand he must make a minimum of 3 skateboards and 2 dolls. The profit on each skateboard is $1.20 and on each doll it is $0.75 2. An orchard owner grows apples and cranberries. Each week he harvests 400 lbs of cranberries and 200 pounds of apples. He uses these fruits to make two different juices: Cranapple and Appleberry. Each gallon of Cranapple uses 6 pounds of cranberries and 2 pound of apples. Each gallon of Appleberry uses 4 pounds of cranberries and 4 pounds of apples. The profits are: Cranapple juice is $0.20 per gallon and Apple berry juice is $0.25 per gallon. He must make at least 4 gallons of Cranapple and 2 gallons of Appleberry. 3. A clothing designer is making polyester skirts and dresses. She has 2400 person minutes of labor available and 1800 yards of fabric to use. Each skirt requires 4 yards of fabric and takes 40 minutes to make. Each dress uses 6 yards of fabric and takes 50 minutes to make. The profit on each skirt is $6.75 and the profit on each dress of $7.25. She must make a minimum of 8 skirts and 12 dresses. 4. A paper recycling company uses scrap cloth and scrap paper to make two different grades of recycled paper. A single batch of grade A paper is made from 25 lbs of scrap cloth and 10 pounds of scrap paper, whereas a single batch of grade B paper is made from 10 pounds of scrap cloth and 20 pounds of scrap paper. The company has 200 pounds of scrap cloth and 240 pounds of scrap paper available. The grade A paper brings a profit of $500 and the grade B paper brings a profit of $250. What amount of each should be made to maximize profits if you must make at least 1 batch of each?