1.Suppose a restaurant operated by an outside company which sells buffet dinners
ID: 3325538 • Letter: 1
Question
1.Suppose a restaurant operated by an outside company which sells buffet dinners on campus has 150 seats. On any given night each seat can be used by only person so a maximum of 150 people can visit the restaurant each night. Because the buffet is already cooked, the cost of keeping the restaurant open for dinner each night is constant at $1,000 regardless of the number of people who visit. We will look at the pricing policy of the restaurant. The following equation describes current demand:
Q = 400 – 10P
Suppose the present price is $28.
How many people eat at the restaurant every night?
What is the revenue? What is the profit?
What is its optimal price? How many people visit the restaurant at this price and what is the revenue? What is the profit?
A consultant proposes an expansion plan to increase the capacity of the restaurant to 200 seats. The expansion will be fully paid for by the university so that the restaurant company will not incur any additional cost from the building project. Should the restaurant expand? Explain your answer.
Suppose the university does not pay the full cost of the expansion and proposes a contract such that the restaurant company has to pay the university $300 every night it is open. Does this information change your answer to part (d) above? Explain.
2.A local toy store produces dolls and its weekly fixed costs are is $500 while its marginal cost per doll is $2.
Daily demand for dolls is given by:
P = 20 – 0.5Q
where P denotes price in dollars and Q denotes daily sales of dolls. Find the store’s profit- maximizing daily output level and price.
At this price, what is the profit generated by dolls every week? Assume that there are 5 days in a week during which production and sales take place.
The store also sells toy cars. However, it does not produce the cars itself. It buys the cars from a wholesale distributor for $10 each. The annual demand for the cars is given by:
D = 2000 – 50P
The store is currently selling the cars for $15 each. What annual profit does the store make from the cars at this price?
The manager proposes doubling the price to $30 claiming that this will increase profits. Is the manager correct? By how much will the annual profit change?
The accountant proposes a smaller price increase to $20 claiming that revenue is maximized at this price. Is the accountant correct?
Who has the better proposal, the accountant or the manager? If you are the owner of the store what price will you set for the cars? Why?
p is price q is quantity
Explanation / Answer
Q1. Now a maximum of 150 people can visit the restaurants, and cost of keeping the restaurant open is 1000$. the demand is given bey the following equation Q = 400 -10P so at a price of 28$ the Q = 120,
(a) Hence 120 people will eat at the restaurant every night,
(b) revenue will be 28 * 120 = 3360$ adn profit will therefore be 3360 - 1000$ = 2260$
(c) Optimal price is when all 150 seats gets filled so 150 = 400 -10P which means P = 400-150 / 10 = 250/10 = 25$ per seat. At this price revenue is 25*150 = 3750$ and profit will be 3750 - 1000 = 2750$ which ismore than the pricing at 28$
(d) If the restaurant is paid for fully by the university for the expansion with no extra cost to the restaurant then the restaurant should definitley as added capacity will increase profit
(e) If restaurant pays 300$ to university for every night it is open then the expansion should not be done, as even though revenue might increase but profits will be lesser.
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