Question

A manufacturer of kitchen appliances is preparing to set the price on a new blender. Demand is thought to depend on the price and is represented by the model

D = 2,500 – 3P

The accounting department estimates that the total cost can be represented by

C = 5,000 + 5D

Develop a mathematical model for the total profit in terms of the price, P. (Using Excel)

Answer 1

As demand decreases as price incrreases, so to maximize profit we cannot just increase price of the blender after a certain level, it will cause loss. Let us make profit as a function of price.

Total Cost = 5000 + 5D, where D = 2500 – 3P
=> Total Cost = 5000 + 5(2500 – 3P) = 17500 – 15P
Total Revenue = DP = 2500P – 3P2

Net Profit = Total Revenue – Total Cost = 2500P– 3P2 – (17500 – 15P)
Net Profit = 2515 P – 3P2 – 17500
Using Quadratic function, this profit will be maximum when P = 2515/6 = 420 approximately. The following Excel sheet and graph also indicate the same.