SOLUTION: The cost to produce 10 units of a product is $40 and the cost to produce 20 units is $70. If cost (C) is linearly related to the number of items, (q), produced, find the linear eq

Question 702561: The cost to produce 10 units of a product is $40 and the cost to produce 20 units is
$70. If cost (C) is linearly related to the number of items, (q), produced, find the linear equation that represents this relationship, then use this equation to determine the cost of producing 17 items. would the formula and equation below be correct?
(difference of c)/(difference of q).
(70-40)/(20-10)=3,
Applying the same slope or ratio to 17,
(C-40)/(17-10)=3,
C-40=3(17-10),
C = 21 + 40 = 61
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The cost to produce 10 units of a product is $40 and the cost to produce 20 units is $70.
If cost (C) is linearly related to the number of items, (q), produced, find the linear equation that represents this relationship,
You have two points relating C and q: (10,40) and (20,70)
slope = (70-40)/(20-10) = 3
Form: C = mq + b
You know m = 3 and C = 40 when q = 10.
Solve for "b":
40 = 3*10 + b
b = 10
Equation:
C(q) = 3q + 10
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then use this equation to determine the cost of producing 17 items.
C(17) = 3*17+10
C(17) = 51+10
C(17) = $61.00
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Cheers,
Stan H.
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