SOLUTION: In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Project

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Question 106088: In planning for a new item, a manufacturer assumes that the number of items produced x and the cost in dollars C of producing these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
Answer by stanbon(48558) (Show Source):
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Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000 to produce. Find the equation that relates C and x.
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You have two points: (100,10000) and (300,22000)
slope = [22000-10000]/[300-100] = 12000/200 = 60
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Form is: Cost = slope*# of items + b
Solve for b by substituting as follows:
10000= 60*100 + b
b = 10000-6000= 4000
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EQUATION:
Cost = 60(# of items) + 4000
C(x) = 60x + 4000
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Cheers,
Stan H.