Question

16. Given the following profit function: π(x) = x3-6x2-3x + 25 where x is the number of days of producing the good. a. interpret (5) b, interpret π, (5) c. based on b, what would you predict sales to be on day 6. d. Using information from a-c, would predicted sales on day 6 be an overestimate or under estimate? Explain?

Answer 1

a.

$\pi (5)=5^{3}-6(5)^{}2-3(5)+25 =125-150-15+25=85$

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b.

$\pi '(5)=3x^{2}-12x-3=3(5)^{2}-12(5)-3=75-60-3=12$

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c.

Since the profits are positive, therefore, the sales on the day 6 will increase.

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d.

The first derivative of profit function is positive. It means that producer should have stopped selling the goods. Therefore, the predicted sales of day 6 will be an overestimate.