- A Restaurant Faces Very High Demand For Its Signature Mousse Desserts In The Evening But Is Less Busy During The Day It 1 (135.16 KiB) Viewed 46 times
explain to me why is optimal profit is 52 and how to calculate it,
Thank you!
A restaurant faces very high demand for its signature mousse desserts in the evening but is less busy during the day. Its manager estimates that (inverse) demand curves are pe = 20 - Qe in the evening and pa = 11 - Qa during the day, where e and d denote evening and daytime. The marginal cost of producing its dessert, MC₁, is $3. Any morning, the restaurant can bring in additional tables and convert its storage space to seating to increase capacity for that day. Creating enough extra capacity to provide one more dessert in the evening or the day costs $5, which is the restaurant's marginal capacity cost, MC 2. = 20 Pe Q₂ 11 Pa Qa = MC₁ 3 = MC₂ 5 MR. 20 2 Qe = MRd 11 2 Qa a) Calculate the prices, marginal revenues, and marginal costs in the evening and daytime, and total marginal costs for Q = 1, 2, ..., 10. Qe Pe MRe Qa Pd MR₁ MC₁ MC₂ MCT 1 $19 $18 1 $10 $9 $3 $5 $8 2 $18 $16 2 $9 $7 $3 $5 $8 3 $17 $14 3 $8 $5 $3 $5 $8 4 $16 $12 4 $7 $3 $3 $5 $8 5 $15 $10 5 $6 $1 $3 $5 $8 6 $14 $8 6 $5 -$1 $3 $5 $8 7 $13 $6 7 $4 -$3 $3 $5 $8 8 $12 $4 8 $3 -$5 $3 $5 $8 9 $11 $2 9 $2 -$7 $3 $5 $8 10 $10 $0 10 $1 -$9 $3 $5 $8 b) Determine the optimal prices for the dessert that the restaurant should charge during the evening hours and during the day, the associated quantities sold, and the total daily profit. The optimal price The optimal price in daytime is $7 when the output is $14 when the output is 6 in the evening is The optimal profit is $52