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.

5000

Step-by-step 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.