Setting the price of a product to maximize profit is a nonlinear problem that could be assigned to a management scientist. Demand D for a product is generally a decreasing function of price P.
When the price is low demand is high but the profit is small because the difference between price and cost C is small. So you can sell a large number but the profit of each is small.
If the price is large you sell very few but make a lot on each one you do sell. Somewhere in between the product of demand and Price-Cost is a maximum.
Assume that the Demand for a certain product decreases linearly with price but increases with the amount of advertising spent according to the following formula:
Demand =100-0.5P+26A0.5
Where A is the amount spent on advertising in thousands of dollars.
Use nonlinear programming to find the optimum value of the price and amount to spend on advertising to maximize the difference between total revenue and the advertising expense assuming a cost of C=$5.
A is the amount spent on advertising in thousands of dollars.
price is P