Question

you are about to introduce a new computer storage technology you have been given demand forecasts for the first two years of its introductio in the market as 1500-0.15p, where p is the selling price in dollars. You wish to find the price that will maximize your profit if the cost per unit is $500, and the fixed cost is $1,000,000

22. The slope of the profit line is given by the function?

23. the price that maximizes the profit is equal to?

24. The maximum possible profit per month is ?

Please, show a process to solve them. do not do only one question.

Answer 1

q = 1500-0.15p => 0.15p = 1500 - q => p = (1/0.15)(1500 - q) => p = 10000 - (1/0.15)q

=> Profit = Total Revenue - Total Cost

=> Profit(Pr) = pq - 1,000,000 - 500q

=> Profit(Pr) = (10000 - (1/0.15)q)q - 1,000,000 - 500q

Slope of profit line is given by:

d(Pr)/dq = 10000 - (2/0.15)q - 500 = 9500 - (2/0.15)q-------Slope of profit line

23)

Profit(Pr) = (10000 - (1/0.15)q)q - 1,000,000 - 500q

First order condition:

d(Pr)/dq = 0 => 10000 - (2/0.15)q - 500 = 9500 - (2/0.15)q = 0

=> q = 0.15*9500/2 = 712.5

=> p = 10000 - (1/0.15)712.5 = 5250

Hence profit maximizing price = 5250

24)

Hence Maximum profit = 5250*712.5 - 1,000,000 - 500*712.5

=> The maximum possible profit per month is 2384375