For the following demand function, find a. E, and b. the values of q (if any) at
ID: 2891148 • Letter: F
Question
For the following demand function, find a. E, and b. the values of q (if any) at which total revenue is maximized. q 37,400-9p a. Determine the elasticity of demand, E. E- (Type an expression using p as the variable.) b. Determine the value of q that maximizes the revenue. Select the correct choice below, and if necessary, fill in the answer box within your choice O A. O B. No values of q maximize total revenue. Total revenue is maximized at about g- (Round to the nearest whole number as needed.)Explanation / Answer
q = 37400 - 9p^2
dq/dp = p/q * dq/dp
dq/dp = -18p
And thus,
dq/dp = p/(37400 - 9p^2) * -18p
dq/dp = (-18p^2)/(37400 - 9p^2) ----> ANS
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q = demand
p = price
So, revenue = pq
R = p(37400 - 9p^2)
R = 37400p - 9p^3
Now, for max revenue, dR/dp = 0 :
dR/dp = 37400 - 27p^2 = 0
p = 37.2180760543205025194
Now, at this pt,
q = 37400 - 9p^2
becomes
q = 37400 - 9(37.2180760543205025194)^2
q = 24933.3333333333333331895749
as in, approx
q = 24933 ----> ANS