# optimzation problem #4

• Aug 12th 2009, 01:30 PM
skeske1234
optimzation problem #4
A chain of stores has been selling a line of cameras for 50 dollars each and has been averaging sales of 8000 cameras a month. They decide to increase the price, but their market research indicates that for each one dollar increase in price, sales will fall by 100.

a) find the demand function

b)find the price that will maximize their revenue
• Aug 12th 2009, 02:06 PM
skeeter
Quote:

Originally Posted by skeske1234
A chain of stores has been selling a line of cameras for 50 dollars each and has been averaging sales of 8000 cameras a month. They decide to increase the price, but their market research indicates that for each one dollar increase in price, sales will fall by 100.

a) find the demand function

b)find the price that will maximize their revenue

let x = number of \$1 price increases

demand function ...

d = 8000 - 100x

revenue = demand * price ...

R = (8000-100x)(50+x)

find dR/dx and determine the value of x that maximizes revenue ... don't forget that the price is (50+x).
• Aug 12th 2009, 03:55 PM
skeske1234
Quote:

Originally Posted by skeeter
let x = number of \$1 price increases

demand function ...

d = 8000 - 100x

revenue = demand * price ...

R = (8000-100x)(50+x)

find dR/dx and determine the value of x that maximizes revenue ... don't forget that the price is (50+x).

ok.. question, your demand function is d=8000-100x