Linear Programming Day #2

1. Linear Programming Day #2 Solutions from hw: #3 max 21000 @ (0,700) #5 max 100 @ (12,4) min 8000 @ (400,0) min 46 @ (3,4) #6 max 40 @ (0,20) last problem: max profit of $192 min 0 @ (0,0) occurs at (6,6)

2. Define variables, write constraints, and write an objective function. ex. Mrs. Smith grows peaches and apples. At least 500 peaches and 700 apples must be picked daily to meet minimum demands from her buyers. The workers can pick no more than 1400 peaches and 1200 apples daily. The combined number of peaches and apples that the packaging department can handle is 2300 a day. If Mrs. Smith makes a profit of $.25 for each apple and $.20 for each peach, how many of each should be picked daily for maximum income? What is the maximum income?

3. Ex. Wheels, Inc. makes mopeds and bicycles. Experience shows that each month they must produce at least 10 mopeds and at least 20 bicycles to meet demand. The factory can produce at most 60 mopeds and at most 120 bicycles in a month. They can make at most 160 vehicles combined. The profit on a moped is $134 and on a bicycle is $30. How many of each should be made each month to maximize weekly profit? What is the maximum profit?

4. Ex. A travel agent is arranging a ski trip for a local ski club. She can provide for at most 10 people, and there must be at least 4 men and 3 women. Her profit is $12.25 for each woman and $15.40 for each man. How many men and how many women will give her the maximum profit? What is the maximum profit?