Homework Soursemanufacturer is planning to sell a new product at the price
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 (250y/(y+4))+(200x/(x+2)) units of the product. If manufacturing costs $170 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
Promotion:
dollars
Development:
dollars
Solution
profit: z=(250y/(y+4))+(200x/(x+2))(300-170)-x-y z=(65000+58498x-x^2)/(x+2)-y-130000/(y+4) to maximize z dz/dx=0 dz/dy=0 so we get x=20sqrt(130)-2=226.04 y=100sqrt(13)-4 =356.56 z=57327.81
