Question

Suppose a company's revenue function is given by R(q)=−q3+320q2R(q)=-q3+320q2 and its cost function is given by C(q)=290+20qC(q)=290+20q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)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)=MP(q)=     

B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)

Answer 1

PART(a):

The given revenue function is,

The given cost function is,

The profit function is given by,

Marginal profit function is given by,

diff wrt q,

PART(b):

For maximum profit, the marginal profit is zero,

after solving above eqn,

To check for maxima, let us find the second derivative given by,

plugin the critical points,

Hence the number of items(in hundreds) which produce maximum profit is given by,

I hope this answer helps,
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