Question

For the cost and price functions​ below, find

​(​a) the​ number, q, of units that produces maximum​ profit;

​(​b) the​ price, p, in dollars per unit that produces maximum​ profit; and

​(​c) the maximum​ profit, P, in dollars.

C(q)=100+20qe^-0.01q ; p=60e^-0.01q

​(a) The​ number, q, of units that produces maximum profit is $__

​(Do not round until the final answer. Then round to the nearest whole number as​ needed.)

​(b) The​ price, p, per unit that produces maximum profit is $__

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

​(c) The maximum profit is $__

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

We are given

cost equation:

price equation:

Revenue:

R=pq

Profit equation:

P=R-C

(A)

we can find derivative

now, we can set it to 0

and then solve for q

..........Answer

(B)

we can plug q=100

..........Answer

(C)

we can plug q=100

..........Answer