9514 1404 393
Answer:
$11,988
Explanation:
A graphing calculator gives you the answer easily.
The minimum unit cost is $11,988.
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The equation for unit cost can be put into vertex form to find the minimum.
C(x) = 0.7x^2 -210x +27738
C(x) = 0.7(x^2 -300x +150^2) +27738 -0.7(150^2)
C(x) = 0.7(x -150)^2 -11,988
This is vertex form:
C(x) = a(x -h)^2 +k . . . . . . . where (h, k) is the vertex.
The vertex of this cost function is (150, 11,988).
The minimum unit cost occurs when 150 engines are produced. That unit cost is $11,988.