A manufacture has been selling 1950 television sets a week at 510 each. A market

Question

A manufacture has been selling 1950 television sets a week at 510 each. A market survey indicates that for each 15 rebate offered to a buyer, the number of sets sold will increase by 150 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 165750 + 170 x, how should it set the size of the rebate to maximize its profit?

Explanation / Answer

a)
(p - 510)/(x - 1950) = -15/150
p - 510 = -0.1x + 195
p = -0.1x + 705

r = px

p = -0.1x + 705
0.1x = 705 - p
x = 7050 - 10p

r = 7050p - 10p^2

dr/dp = 7050- 20p
7050 - 20p = 0

7050 =20p
p = 352.5
rebate =510 - 352.5 = 157.5

f = px - c
f = (-0.1x +705)x - (165750 + 170 x)
f = -0.1x^2 +705x - 165750 -170 x
f = -0.1x^2 + 535x - 165750

df/dx = -0.2x +535
-0.2x + 535 = 0
x = 2675 sets

p = -0.1*2675 + 705
p = 375
rebate = 510 - 437.5 = 72.5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.