Problems
A small backpack manufacturer carries four different models of backpacks, made of canvas, plastic, nylon, and leather. The bookstore, which will exclusively sell the backpacks, expects to be able to sell between 15 and 40 of each model. The store has agreed to pay $35.50 for each canvas backpack, $39.50 for each plastic backpack, $42.50 for each nylon backpack, and $69.50 for each leather backpack that can be delivered by the end of the following week.
One worker can work on either canvas or plastic, can complete a backpack in 1.5 hours, and will charge $7.00 per hour to do the work. This worker can work a maximum of 90 hours during the next week. Another worker can sew backpacks made of nylon fabric. He can complete a bag in 1.7 hours, will charge $8.00 per hour to work, and can work 42.5 hours in the next week. A third worker has the ability to sew leather. He each can complete a book bag in 1.9 hours, will charge $9.00 per hour to work, and can work 80 hours during the next week. The following table provides additional information about each backpack. What is the best combination of backpacks to provide the store to maximize the profit?
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Backpack Model
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Material Required (square yards)
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Material Available (square yards)
|
|
Canvas
|
2.25
|
200
|
|
Plastic
|
2.40
|
350
|
|
Nylon
|
2.10
|
700
|
|
Leather
|
2.60
|
550
|