Question 136363: I do not understand how to set up this equation.
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?
Thank you very much!!!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
:
Assuming this is linear relationship
:
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 = 
:
m =  = 
:
Use the point/slope formula: y - y1 = m(x - x1)
:
y - 25 = (x - 100)
y - 25 = x - 
y = x - 12 + 25
y = x + 13
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Using the above equation: x = 130
y = (130) + 13
y = 15.6 + 13
:
y = $28.60 profit for 130,000 chips
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