dots restaurant must decide between two technology processes in their kitchen. they only serve dinner after…

dots restaurant must decide between two technology processes in their kitchen. they only serve dinner after 4 p.m. on a small island called sanibel. the restaurant is open 250 days per year. dot and her husband, ham, are retired. they became bored playing golf five times a week and decided to open this boutique restaurant. process a uses an induction oven and microwave process with a fixed cost of $47,000 and a variable cost of $4.14 per meal. process b uses a gas - fired oven process with heating lamps with a fixed cost of $29,000 and a variable cost of $5.14 per meal. process a speeds up cooking and delivery time. the average selling price per meal is $31.29.\na. what is the break - even quantity? round your answer to the nearest whole number.\n12857 meals\nb. if the restaurant manager expects to sell 8,000 meals, which option, a or b, is best? round your answers to the nearest dollar.\ncost of option a: $80120\ncost of option b: $73320\nso, option b is the best option.\nc. is the restaurant profitable if they purchase the process option you recommend in part (b)? enter your answer as a positive value. round your answer to the nearest dollar.\nthe restaurants profit is $

dots restaurant must decide between two technology processes in their kitchen. they only serve dinner after 4 p.m. on a small island called sanibel. the restaurant is open 250 days per year. dot and her husband, ham, are retired. they became bored playing golf five times a week and decided to open this boutique restaurant. process a uses an induction oven and microwave process with a fixed cost of $47,000 and a variable cost of $4.14 per meal. process b uses a gas - fired oven process with heating lamps with a fixed cost of $29,000 and a variable cost of $5.14 per meal. process a speeds up cooking and delivery time. the average selling price per meal is $31.29.\na. what is the break - even quantity? round your answer to the nearest whole number.\n12857 meals\nb. if the restaurant manager expects to sell 8,000 meals, which option, a or b, is best? round your answers to the nearest dollar.\ncost of option a: $80120\ncost of option b: $73320\nso, option b is the best option.\nc. is the restaurant profitable if they purchase the process option you recommend in part (b)? enter your answer as a positive value. round your answer to the nearest dollar.\nthe restaurants profit is $

Answer

Explanation:

Step1: Recall break - even formula

Let $Q$ be the break - even quantity. The total cost for process A is $C_A = 47000+4.14Q$, and for process B is $C_B=29000 + 5.14Q$. At break - even, $C_A=C_B$. So, $47000+4.14Q=29000 + 5.14Q$.

Step2: Solve for $Q$

First, subtract $4.14Q$ from both sides: $47000=29000 + 5.14Q-4.14Q$. Then simplify to get $47000=29000 + Q$. Subtract 29000 from both sides: $Q=47000 - 29000=18000$ meals.

Step3: Calculate cost for 8000 meals for Option A

$C_A=47000+4.14\times8000=47000 + 33120=80120$

Step4: Calculate cost for 8000 meals for Option B

$C_B=29000+5.14\times8000=29000 + 41120=70120$

Step5: Calculate profit for Option B

Revenue from selling 8000 meals is $R = 31.29\times8000=250320$. Cost of Option B is $C_B = 70120$. Profit $P=R - C_B=250320-70120 = 180200$

Answer:

a. 18000 b. Cost of Option A: $80120$, Cost of Option B: $70120$, So, Option B is the best option. c. 180200