Question

A company that sells toys models their profit with the function

P(x) = −4x3 + 32x2 − 64. Their profit P, in thousands of dollars,
is a function of the number of toys sold x measured in hundreds.
What do the key features of the graph reveal about the profits?
What is the maximum profit the company can make?

Answer 1

9514 1404 393

Answer:

a) profit has a typical curve: negative at low volume, and again at very high volume.

b) $239,407

Explanation:

a) The graph is negative below x=1.58, so the break-even point is 158 toys sold. The profit declines steeply above 533 toys sold, to again go negative for 774 toys sold. This sort of curve seems fairly typical.

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b) The profit is a maximum of $239,407 when 533 toys are sold.