1. ## Demand problem

A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

a) Find the demand function p(x), where x is the number of the television sets sold perweek. p(x) =

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?

A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

a) Find the demand function p(x), where x is the number of the television sets sold perweek. p(x) =

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?
A prive reduction of $29 increases sales by 290, so the sales chanve by -10 per$ increase in price. So assume a linear reation between demand and price:

x=-10 p +c

where x is the demand, and p the price, then as 1650 are sold at a price of \$420 c=5850, and the demand function is:

x=-10 p + 5850.

Inverting this we get:

p(x)=585-0.1x

RonL

A manufacture has been selling 1650 tv sets a week at 420 each. A market survey indicates that for each 29 rebate offered to a buyer, the number of sets sold will increase by 290 per week.

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?

c) If the weekly cost function is 115500 + 140x. How should it set the size of the rebate to maximize its profit?
Revenue is:

r=x p(x)

maximise this to find the price/sales that maximise revenue, and then calculate the corresponding discount.

Profit is:

prft(x) = r - costs =x p(x) - (115500 + 140x)

Now proceed as before

RonL