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Alex17521 [72]
4 years ago
15

Assume that the situation can be expressed as a linear cost function. Find the cost function in this case. Marginal​ cost: ​$40​

; 180 items cost ​$9500 to produce. The linear cost function is ​C(x) = ____.
Mathematics
1 answer:
Y_Kistochka [10]4 years ago
4 0

Answer:

The linear cost function is C(x)=40\cdot x+2300

Step-by-step explanation:

A linear cost function expresses cost as linear function of the number of items

C(x)=mx+b

Here, C(x) is the total cost, and x is the number of items. The slope m is called the marginal cost and b is called the fixed cost.

From the information given we know

m = $40 and C(180) = $9500

We can find the value of b in this way

C(x)=mx+b\\C(180)=\$40\cdot 180+b=\$9500

solving for b

b=\$9500-\$40\cdot 180=\$2300

The linear cost function is C(x)=40\cdot x+2300

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