Nonlinear Price Function

Usually, high-volume discount retailers such as Restaurant Depot, Sam’s Club, and Costco offer bulk discounts. The price often decreases exponentially when purchasing in very large quantities. Assume that the price function follows an exponential relationship with demand, as shown below.

Calculate the following using both calculus and MS Excel:

1. Demand that maximizes 

   • revenue

   • profit

2. Maximum 

   • revenue

   • profit

3. Breakeven points

4. Develop MS Excel graphs

Answer

1. Demand Maximizing 

   • Revenue = 100 units

   • Profit = 92 units

2. Maximum 

   • Revenue = $5,518 

   • Profit == $4,040

3. Breakeven Demand 

= between 8 and 287 units 

4. Figure 2-16 shows the solution generated using MS Excel for a wide range of possible demand scenarios.