Suppose a company's revenue function is given by R(q) = - q^3 + 220q^2 and its cost function is given by C(q) = 500 + 13q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)
MP(q) =
B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)

A) MP(q) = -3q² + 440q - 13

B) 146.64 units.

Step-by-step explanation:

The profit function is given by the revenue minus the cost function:

A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:

B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:

Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.

four boxes of pizza

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