Question

Hey im confused on how to solve this. Can Anyone help me?

Answer 1

Answer:

The minimum unit cost is $9374.

Step-by-step explanation:

The unit cost C for making x engines is given by the quadratic function:

$C(x)=0.3x^2-162x+31244$

We want to determine the minimum unit cost.

Since this is a quadratic function with a positive leading coefficient, the minimum value will be its vertex. The vertex of a quadratic can be found using the following formulas:

$\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = 0.3, b = -162, and c = 31244.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(-162)}{2(0.3)}=\frac{162}{0.6}=270$

In other words, in order to achieve the minimum cost, only 270 engines must be made.

Then to find the minimum cost, substitute the value back into the function. So:

$C(270)=0.3(270)^2-162(270)+31244=\ 9374$

The minimum unit cost is $9374.