An aircraft factory manufactures airplane engines. the unit cost (the cost in dollars to make each airplane engine) depends on the number of engines made. if engines are made, then the unit cost is given by the function . what is the minimum unit cost?

Consider the following explanation

Explanation:

We will use derivative to get minimum cost.

To get minimum cost, we will solve C'(x) =0 for x.

C(x)=0.1x2-20x+12942

C'(x)=0.2x-20

C'(x)=0   =>    x= 100 ( Critical point)

Now apply second derivative test to decide minimum value of C(x).

C"(x)=0.2

At x=100, C"(x) = 0.2 >0 . Hence C(x) will be minimum when x=100.

So Cmin = 0.1(100)2-20(100) + 12942.

  Cmin = 11942

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