Question

An aircraft factory manufactures airplane engines with a unit cost function ( C(x) = 0.2x^2 - 136x + 37,970 ). What is the minimum unit cost?

Options:
A) $37,970
B) $37,834
C) $38,205
D) $37,715

Answer 1

To find the minimum unit cost given the quadratic unit cost function C(x) = 0.2x^2 - 136x + 37,970, we calculate the vertex of the parabola. This occurs at x = 340, and substituting back into the unit cost function, the minimum unit cost is $37,834.

Step-by-step explanation:

The question involves finding the minimum unit cost for manufacturing airplane engines, given the unit cost function C(x) = 0.2x^2 - 136x + 37,970. To find the minimum unit cost, we need to calculate the vertex of the quadratic function, which occurs at x = -b/(2a) for a function in the form ax^2 + bx + c. Here, a = 0.2 and b = -136.

Calculating the x-coordinate of the vertex gives us x = -(-136) / (2 * 0.2) = 136 / 0.4 = 340. Plugging x = 340 back into the unit cost function provides us with the minimum unit cost C(340) = 0.2(340)^2 - 136(340) + 37,970. After calculating, we find that the minimum unit cost is $37,834, which corresponds to option B).