A manufacturer has been selling 1800 television sets a week at $360 each. A mark

Question

A manufacturer has been selling 1800 television sets a week at $360 each. A market survey indicates that for each $23 rebate offered to a buyer, the number of sets sold will increase by 230 per week.
a) Find the demand function p(x), where x is the number of the television sets sold per week.
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 $108000+120x, how should it set the size of the rebate to maximize its profit? $

Explanation / Answer

when price= 360 demand= 1800

when price= 337 demand= 2030

so equation of demand can be written as

p-360=(360-337/1800-2030)(q-1800)

or

p-360= 180-x/10

p=540-x/10

b).Revenue= px

= (540-x/10)*x

for maxima dR/dx=0

540-2x/10=0

or x= 2700

so p= 540-270

= 270

so rebet should be 360-270

= $90 per unit

c). MC=120

so for maximising profit P=MC

so p=120 thus rebet= $240 per unit

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