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 $9 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 $12 per 50-pound bag and sells for $20.99. The company currently sells 26,000 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 $20.99. The quantity of RoverPlus and the quantity of Royal Dog Food that will be sold at various prices for Royal are estimated as:

For example, if RoverPlus is priced at $9.99, the company will sell 36,000 bags of RoverPlus and 12,000 bags of Royal at $20.99. If the company prices RoverPlus at $17.99, it will sell 6,000 bags of RoverPlus and 22,000 bags of Royal at $20.99. This is 4,000 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?

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Price Quantity RoverPlus Quantity Royal RoverPlus $ 9.99 36,000 12,000 35,500 12,300 $10.99 $11.99 35,000 12,500 $12.99 34,000 13,000 14,000 $13.99 31,000 $14.99 26,000 15,000 $15.99 16,000 16,000 $16.99 11,000 20,000 $17.99 6,000 22,000