Solve for the cost

Question

An aircraft factory manufactures airplane engines. The unite cost C ( the cost in dollars to make each airplane engine) depends on the number of engines made. If x is the number of engines made, then the unit cost is given by the function C(x)=0.8x^2-160x+26,848. What is the minimum unit cost? not rounded

Answer 1

If you have calculus the minimum occurs when the derivative C'(x) = 0, i.e.

1.6x - 160 = 0

The minimum cost will occur when x = 100.

 

If you don't have calculus, then you need to know that the vertex of a parabola (quadratic equation) occurs when x = -b/2a, in this case 160/(2 * .8) = 100.

 

I will leave it you to substitute the x = 100 into C(x) to get the minimum cost.