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Question 398034: A semiconductor manufacturer seeks to maximize its profits. Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Testing indicates that they can produce 100,000 chips per week at a cost of $40 per chip, and sell them for $65 per chip. They also find that they can produce 125,000 chips per week at a cost of $35 per chip, and sell them for $63 per chip. How much profit can they expect to earn if they produce 130,000 chips per week?
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You have two points relating production and profit:
(100000,25) and (125000,28)
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slope = (28-25)/(125k-100k) = 3/25k = 0.00012
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Form: y = mx+b
25 = (0.00012)(10000) + b
25 = 33+b
b = -8
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Equation:
f(x) = (0.00012)x-8
How much profit can they expect to earn if
they produce 130,000 chips per week?
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f(130000) = (0.00012)(130000) - 8
f(130000) = 15.6-8 = $7.60
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Cheers,
Stan H.
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