Suppose the cost function for producing gadgets is C(q)=0.05q2+3q+48.

Question

a. At what production level is the maximal profit achieved if each item is sold for 9 dollars? ______ items.

b. What is the maximum profit if each item is sold for 9 dollars? ______ dollars.

Answer 1

revenue = price * quantity, so
r(q) = 9q
profit = revenue - cost, so
p(x) = 9q - 0.05q^2 - 3q - 48 = -0.05q^2 + 6q - 48
dp/dq = -0.1q + 6
max profit is $132 at q=60