(a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost (b) If C(x) 16,000 500x 1 6x 2 0 004x 3 is the cost function and p(x) 1700 7x is the demand function, find the production level that will maximize profit

Question: (a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost. (b) If C(x) = 16,000 + 500x

(a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost.
(b) If C(x) = 16,000 + 500x - 1.6x² + 0.004x³ is the cost function and p(x) = 1700 - 7x is the demand function, find the production level that will maximize profit.

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