Question
Asked Mar 18, 2020
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For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per unit that
produces maximum profit; and c) the maximum profit, P.
C(q) = 80 + 18q; p = 66 – 2q
a) The number, q, of units that produces maximum profit is q =
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For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per unit that produces maximum profit; and c) the maximum profit, P. C(q) = 80 + 18q; p = 66 – 2q a) The number, q, of units that produces maximum profit is q =

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Expert Answer

Step 1

Given

Cost function C(q) = 80 + 18q

Price function p = 66 – 2q

Step 2

Find the revenue and profit functions

Calculus homework question answer, step 2, image 1

Step 3

a) Clearly the above profit function is of the form of quadratic function f(x) = ax2 + bx + c and maximum occurs at the vertex point x = -b/2a.

Find the number of units that produces maximum profit.

Calculus homework question answer, step 3, image 1

Therefore, the number, q, of units that produces maximum pro...

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