In Problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose

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In Problem, cost, revenue, and profit are in dollars and x is the number of units.

Suppose that the total revenue function for a product is R(x) = 50x and that the total cost function is

C (x) = 1900 + 30x + 0.01x2.

(a) Find the profit from the production and sale of 500 units.

(b) Find the marginal profit function.

(c) Find M̅P̅ at x = 500 and explain what it predicts.

(d) Find P (501) - P (500) and explain what this value represents.

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