A Manufacturer Is Planning to Sell a New Product at the Price

Short Answer

A manufacturer is planning to sell a new product at the price of $80 per unit and estimates that if x thousand dollars is spent on development and y thousand dollars is spent on promotion, approximately $\frac { 360 y } { y + 7 } + \frac { 180 x } { x + 14 }$ units of the product will be sold. The cost of manufacturing the product is $70 per unit. If the manufacturer has a total of $360,000 to spend on development and promotion, how should this money be allocated to generate the largest possible profit? [Hint: Profit equals (number of units)(price per unit minus cost per unit) minus total amount spent on development and promotion.]