Answer:
P = 38
Q = 95,000
max profit: 2,310,000
Explanation:
cost: 540,000 + 40Q
marginal cost: dC/dQ = 40
based on the current price and sales and the marketing studies we build for the inverse demand function:
Q = aP + b
if P = 70 then, Q = 15,000
if P = 68 then, Q = 20,000
-2P = + 5,000Q
-1P then, 2,500 Q
15,000 = -2,500(70) + b
b = 190,000
so Q = -2,500P + 190,000
revenue; P x Q
P x (-2,500P + 190,000)
-2,500P2 +190,000P
marginal revenue: dR/dQ = -5,000P + 190,000
<u></u>
<u>max profit at MR = MC </u>
40 = 190,000 - 5,000P
189,960 / 5,000 =37.992 = 38
Q = -2,500(38) + 190,000 = 95,000
<u></u>
<u>Profit:</u>
(70 - 40) 95,000 - 540,000 = 2,850,000 - 540,000 = 2,310,000
