Question 136363
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?
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Assuming this is linear relationship
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Profit at 100,000: 65-40 = $25
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Profit at 125,000: 63-35 = $28
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Let x = no. of chips in 1000's; (Sorry, I made a mistake here, it should be x)
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x1 = 100, y1 = 25
x2 = 125, y2 = 28
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Using the slope formula: m = {{{(y2 - y1)/(x2 - x1)}}}
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m = {{{(28 - 25)/(125 - 100)}}} = {{{3/25}}}
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Use the point/slope formula: y - y1 = m(x - x1)
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y - 25 = {{{3/25}}}(x - 100)
y - 25 = {{{3/25}}}x - {{{300/25}}}
y = {{{3/25}}}x - 12 + 25
y = {{{3/25}}}x + 13
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Using the above equation: x = 130
y = {{{3/25}}}(130) + 13
y = 15.6 + 13
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y = $28.60 profit for 130,000 chips