Determining the Profit-Maximizing Price RoverPlus a pet product superstor

Determining the Profit-Maximizing Price

RoverPlus a pet product superstore is considering pricing a new RoverPlus-labeled dog food. The company will buy the premium dog food from a company in
Indiana that packs the product with a RoverPlus label. Rover pays $7 for a 50-pound bag delivered to its store.

The company also sells Royal Dog Food (under the Royal Dog Food label) which it purchases for $10 per 50-pound bag and sells for $17.99. The company
currently sells 26000 bags of Royal Dog Food per month but that is expected to change when the RoverPlus brand is introduced.

The company will continue to price the Royal Dog Food brand at $17.99. The quantity of RoverPlus and the quantity of Royal Dog Food that will be sold at
various prices for Royal are estimated as:

Price RoverPlus

Quantity RoverPlus

Quantity Royal

7.99

36000

12000

8.99

35500

12300

9.99

35000

12500

10.99

34000

13000

11.99

31000

14000

12.99

26000

15000

13.99

16000

16000

14.99

11000

20000

15.99

6000

22000

For example if RoverPlus is priced at $7.99 the company will sell 36000 bags of RoverPlus and 12000 bags of Royal at $17.99. If the company prices
RoverPlus at $15.99 it will sell 6000 bags of RoverPlus and 22000 bags of Royal at $17.99. This is 4000 fewer bags of Royal than is currently being
sold.

Required

a. Calculate the profit-maximizing price for the RoverPlus brand taking into account the effect of the sales of RoverPlus on sales of the Royal Dog Food
brand.

b. At the price calculated in part a what is the incremental profit over the profit earned before the introduction of the RoverPlus-branded dog food?