Rover Plus, a pet product superstore, is considering pricing a new Rover Plus-labeled dog food. The company will buy the premium dog food from a company in Indiana that packs the product with a Rover plus 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 26,000 bags of RoyalDog Food per month, but that is expected to change when the Rover Plus brand is introduced.
The company will continue to price the Royal Dog Food brand at $1 7.99. The quantity of Rover Plus and the quantity of Royal Dog Food that will be sold at various prices for Royal are estimated as:
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For example, if Rover Plus is priced at $7.99,the company will sell 36,000 bags of Rover Plus and 12,000 bags of Royal at $17.99. If the company prices Rover Plus at $15.99, it will sell 6,000 bags of Rover Plus and 22,000 bags of Royal at $1 7.99.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 Rover Plus 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 Rover Plus-branded dog food?