1 point) A manufacturer is planning to sell a new product at the price of $300 p

Question

1 point) A manufacturer is planning to sell a new product at the price of $300 per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, consumers will buy approximately ((400y)/(y+1))+((500x)/(x+4)) units of the product. If manufacturing costs $130 per unit, how much should the manufacturer spend on development and how much on promotion to generate the largest possible profit from the sale of this product?

Promotion: ? dollars
Development: ? dollars

Explanation / Answer

P = (40000y)/(y+1))+((50000x)/(x+4))-x-y

dP/dx = 200000/(x+4)^2 - 1

d^2P/dx^2 =- 400000/(x+4)^3

dP/dy = 40000 /(y+1)^2-1

d^2P/dy^2 = -80000/(y+1)^3

(x+4)^2 = 200000

x+4 = 200 root 5

x = 200 root 5 - 4

(y+1)^2= 40000

y = 199

local maxima (200 root 5 -4 , 199)

Promotion = 170* 443.21 = 75346.311$

Development= 199*170 = 33830$

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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