What’s the minimum unit cost?

Question

An aircraft factory manufactures airplane engines. The unit cost C (cost in dollars to make each airplane engine) depends on the number of engines made. If X engines are made, then the unit cost is given by the function C(x)=0.9x^2-540x+94,751. What is the minimum cost? Do not round your answer.

Answer 1

The function is given in the form of the quadratic formula ax² + bx + c. If we find the vertex, this will allow us to find the lowest (minimum) point of the parabola. To find the vertex, we can use the formula -b/2a.

Vertex: -(-540) / 2(0.9) = 300

This gives us the x value of our vertex. This means at a minimum, 300 airplane engines must be made. Now we plug in x = 300 into C(x) to find the minimum cost.

C(300) = 0.9(300)² - 540(300) + 94751

C(300) = 13751

Thus, the minimum cost is $13,751.