Question

The cost, in millions of dollars, for a company to manufacture x thousand speed boats is given by the function C(x) = 3x2 - 30x + 175. Find the number of speedboats that must be produced to minimize the cost.

Answer 1

5000

Explanation:

In vertex form, the cost function is ...

C(x) = 3(x² -10x) +175 = 3(x² -10x +25) +175 -3(25)

C(x) = 3(x -5)² +100

The vertex is at x=5, so the cost function will be minimized when 5000 speed boats are produced.