The manufacturing company makes 2 kinds of lacrosse sticks. Each Type A stick re

Question

The manufacturing company makes 2 kinds of lacrosse sticks. Each Type A stick requires 2 labor-hours for cutting, 1 labor-hour for stringing, 2 labor-hours for finishing, and is sold for a profit of $8. Each Type B stick requires 1 labor-hour for cutting, 3 labor-hours for stringing, 2 labor-hours for finishing, and is sold for a profit of $10. Each day, the company has available 120 labor-hours for cutting, 150 labor-hours for stringing, 140 labor-hours for finishing. How many lacrosse sticks of each type should be manufactured each day to maximize profits? What is the maximum daily profit that can be earned?

Explanation / Answer

Method to solve this question. I hope it will be helpful P = -3x2 + 36x - 72 first find the derivative dP/dx = - 6x + 36 when dP/dx = 0 ; x = 6 d^2P/dx^2 = - 6 ie d^2P/dx^2 < 0 meaning when x = 6 P will be maximum when x = 6. by plugging in this to the given function P = -3(36) +36(6) - 72 = - 108 + 216 - 72 = 216 - 180 = 36 the maximum profit is 36 thousand

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