Question

A supply company manufactures copy machines. The unit cost c (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function c(x) = 0.3x² - 168x + 33,822. How many machines must be made to minimize the unit cost?

Answer 1

To minimize the unit cost, 280 machines must be made.

Step-by-step explanation:

To minimize the unit cost, we need to find the minimum value of the function c(x) = 0.3x² - 168x + 33,822. This is a quadratic function, and the minimum value occurs at the vertex. To minimize the unit cost for manufacturing copy machines, we need to find the vertex of the quadratic function given by c(x) = 0.3x² - 168x + 33,822.

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a = 0.3 and b = -168.

Substituting the values into the formula, we have x = -(-168)/(2*0.3) = 280.

Therefore, to minimize the unit cost, 280 machines must be made.