Alice runs a restaurant and it is only open on Wednesdays and Saturdays. Her tot

Question

Alice runs a restaurant and it is only open on Wednesdays and Saturdays. Her total cost is TC=10+q2 where q is number of meals served per day. Her restaurant is a price taker. A meal is sold at $12 on Wednesday and $20 on Saturday.

a. Get her average cost per day and marginal cost per day.

b. How many meals does she serve on Wednesday to maximize profit? And Saturday? How much is her profit each day? Per week?

c. A newspaper noticed the price difference on different days and reported it. Now to make consumers happy all restaurants in the town have to sell meals for $16 regardless of the days. Calculate Alice’s optimal number of meals to serve and her profit each day and per week.

d. Still assume the meals are sold at $16 each day. Now Alice has to hand in 10% of her profit as income tax to the government. How many meals should she serve each day? How much is her profit after tax?

e. Still assume the meals are sold at $16 each day. Now suppose that due to competition all restaurants serve a free dessert with each meal. This costs Alice $2 for each meal she serves. Calculate her problem and profit each day and per week (no tax and her restaurant opens Wed. and Sat.).

Since the question has too many parts, to make it convenient for grading, write your answers here (values/functions only, no details or procedures):

a. AC= MC=

b. Number of meals on Wednesday: Number of meals on Saturday: Profit on Wednesday: Profit on Saturday: Profit per week:

c. number of meals per day: number of meals per week: profit per day: profit per week:

d.number of meals per day: profit after tax per day:

e. number of meals per day: number of meals per week: profit per day: profit per week:

Explanation / Answer

Average cost per day will depends on Quantity of meal sold

So AVC= (10+q^2)/q -----------(a)

For MC= CHange in total cost/ change in quantity

B) to get profit on wednesday

she should have, (12*q) - (10+q^2) >0 , where q is quantity iof meal served.

-q^2+12q-10>0   

solve the quadratic equation= you will get q= 11.09 and 0.9 so technically .9 meal is not possible so we wil go with 11.09 that atleast more than 11 meals shouldbe served to get the profit.

same logic for saturday can be applied/

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.