4) Chapter 13, problem 33 (page 598)

Given the following list of items

a) classify the items as A, B, or C

b) Determine the economic order quantity for each item (round to the nerest whole unit)

(a) One day, Mary went to a boutique and tried on a dress displayed on the shelf of the
shop. Then, she felt that the dress was not very comfortable and put it back on the
shelf. However, the salesperson insisted Mary needed to pay for the dress because
she already had a contract with the shop.
Peter is the shopkeeper of a pet shop. Last week, Peter lost one of his Persian cats
when taking it for bathing at his shop. He immediately put up a notice on the wall
of his pet shop stating a reward of $1,000 for return of his cat. Recently, when Mary
walked along the street, she found Peter’s lost cat accidentally. Luckily, the cat
wore a necklace with details of Peter’s name and shop address. After Mary returned
the cat to Peter, she discovered the notice on the wall and demanded the reward of
$1,000.
Required:
(i) Advise Mary whether she is legally bound to buy the dress in the boutique. You
are required to cite a relevant case in your explanation.
(ii) Advise Peter whether he is legally bound to pay the reward to Mary. You are
required to cite a relevant case in your explanation.
(b) Ada contracted with Brian to repair her car for $5,000 and to complete the work
within one week. Later, Brian told her that the repair work was very sophisticated
and Ada promised to pay him an extra amount of $500.
Required:
Advise Brian whether Ada is legally bound to pay him the extra amount of $500.
You are required to cite relevant case(s) in your explanation.

A large corporation is interested in predicting a measure of job satisfaction among it employees. They have collected data on 15 employees who each supplied information on job satisfaction, level of responsibility, number of people supervised, rating of working environment and year of service.

Please write out the regression equation of using all predictors and explain the equation.

Which predictor(s) is(are) very important predictor(s) to predict job satisfaction? Why do you select it (them)?

Use the important predictors to form a regression equation and compare this equation with the previous calculated one.

Report all relevant results.

SMU Corp. has future receivables of 4,000,000 New Zealand dollars (NZ$) in one year. It must decide whether to use options or a money market hedge to hedge this position. Use any of the following information to make the decision. Verify your answer by determining the estimate (or probability distribution) of dollar revenue to be received in one year for each type of hedge.

      Spot rate of NZ$ = $.54

      One‑year call option: Exercise price = $.50; premium = $.07

      One‑year put option: Exercise price = $.52; premium = $.03

                                                                                    U.S.     New Zealand

            One‑year deposit rate                                        9%           6%

            One‑year borrowing rate                                    11             8

                                                                                    Rate    Probability

            Forecasted spot rate of NZ$ $.50           20%

                                                                                       .51           50

                                                                                       .53 30

The following data refers to the number of logging operations working in a stretch of tropical rainforest. Excluding externalities, the private cost of a logging operation is $25 thousand per week. Logs sell for $1 a piece. Fill in the chart below.                    

1. What is the number of logging operations in the forest that maximizes total profits in the industry (ignoring externalities)? How much total resource rent is generated at this level of harvest?

2. With open access to the forest, how many folks will wind up logging? With open access, will there be any resource rent earned by the loggers?

3. Which of the following are externalities associated with logging?

___ Loss of genetic material for medical or agricultural applications

___ Low wages for forestry workers

___ Release of carbon-dioxide stored in the “carbon sink” of the forest

___ Building of roads by the companies to access timber

4. Suppose the total externalities associated with deforestation could be valued at $10,000 per operation. What is the efficient (socially optimal) number of operators? What is the open access number of operators?

5. Suppose access to the forest is controlled by a (perfectly enforced) fee system. What (weekly) fee would have to be charged to insure an efficient harvest level?

After graduating from UTD at age 25, John got his first job at Goldman Sachs with an annual salary of $60,000 a
year and a one-time signing bonus of $25,000. He bought a car using his signing bonus. Goldman Sachs offers a
401K retirement investment plan that will match employee’s contribution up to 10%. For example if John invests
1% in the 401K account, Goldman Sachs will put in another 1% into his account. John is expecting an annual
salary increase of 2.4% (APR on a monthly base. For simplicity, assume that the growth will start in the second
month). Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base).
(Assume the beginning of age 25 is month 0 and salary is paid at the end of each month, i.e., beginning of age 65 is
the last period)
(a) What percentage of salary should John invest in his 401K account in order for him to have $2 million in the
account when he retires in 40 years?
(b) At the same contribution rate, if he retires in 35 years instead, how many percent less money will John have?
(c) Instead of buying a nice car, he brought a used car for $10,000, and saved the rest of signing bonus in a separate
investment account for retirement that pays 9.6% annual interest (APR on a monthly base). If John wants to
have $2 million when he retires in 35 years, what percentage of salary should John invest in his 401K account?After graduating from UTD at age 25, John got his first job at Goldman Sachs with an annual salary of $60,000 a
year and a one-time signing bonus of $25,000. He bought a car using his signing bonus. Goldman Sachs offers a
401K retirement investment plan that will match employee’s contribution up to 10%. For example if John invests
1% in the 401K account, Goldman Sachs will put in another 1% into his account. John is expecting an annual
salary increase of 2.4% (APR on a monthly base. For simplicity, assume that the growth will start in the second
month). Suppose, the 401K investment plan will earn him an annual return of 8.4% (APR on a monthly base).
(Assume the beginning of age 25 is month 0 and salary is paid at the end of each month, i.e., beginning of age 65 is
the last period)
(a) What percentage of salary should John invest in his 401K account in order for him to have $2 million in the
account when he retires in 40 years?
(b) At the same contribution rate, if he retires in 35 years instead, how many percent less money will John have?
(c) Instead of buying a nice car, he brought a used car for $10,000, and saved the rest of signing bonus in a separate
investment account for retirement that pays 9.6% annual interest (APR on a monthly base). If John wants to
have $2 million when he retires in 35 years, what percentage of salary should John invest in his 401K account?

The company you are working for has decided to put on a banquet to raise money for a charity and must decide between two catering services to supply the food and servers. You have been assigned to the Banquet Planning Committee. Simplify completely.

Research Provided

The company's research department has provided the following estimates.

• A demand of 230 banquet attendees can be expected at a dinner plate price of $80.00 each. A demand of 370 banquet attendees can be expected at a dinner plate price of $45.00 each.

• Catering Service A has a fixed cost of $1,900 and a marginal cost of $30 for each plate.

• Catering Service B has a fixed cost of $3,000 and a marginal cost of $22 for each plate.

• Costs for both caterers include the food, drinks, plates, utensils, tablecloths, glasses, crew, and cleanup.

• Dinner plates will only be sold as an entire unit. To justify company resources and to ensure the event will benefit the charity, the CEO insists the tickets be sold for no less than $40. All profits will go toward a charity of the committee's choosing.

• Additional spontaneous donations to the charity will be accepted the night of the banquet. Studies estimate that 5% will give $5, 23% will give $20, 18% will give $50, 7% will give $100, and 2% will give $500.

Analysis

Each team should perform the following analyses:

1. Assume the price-demand function is linear. Use the research estimates to find the relationship between the price p, and the number of banquet attendees demanded, x. Find the relevant domain.

2. Find the revenue function, R(x), in terms of the number of banquet attendees x. Find the relevant domain by considering realistic limitations on the number of attendees and on price. Sketch a graph on the work page.

3. Assume the cost function is linear and use the research estimates to find the cost function for each of the two possible catering services in terms of the number of banquet attendees x. Sketch a graph on the work page.

4. Determine the break-even quantities for each of the two possible catering services.

5. Find the Profit function, P(x), for each of the two possible catering services in terms of the number of banquet attendees x.

6. If it is projected that there will be 100 tickets sold at a dinner price of $112.50, which catering service should the committee recommend in order to earn the most profit for the charity?

7. Decide which catering service your company should choose if the projections yield 200 attendees. Include the ticket price at this demand.

8. Find the average cost function for Catering Service A. Evaluate the average cost per attendee if 50 tickets are purchased. Evaluate the average cost per attendee if 400 tickets are purchased.

9. On average, how much can you expect to receive in spontaneous donations for each banquet attendee? (Determine the per person expected value (weighted average) of donations.) Which charity does the committee recommend for receipt of banquet donations?

10. Overall recommendations: Which catering service does your committee recommend in order to obtain the most profit for the charity? How many people should attend the banquet to earn that profit and what profit can be expected from the banquet ticket sales? What price would you recommend for each dinner plate (ticket)? What dollar amount is expected from spontaneous donations? What will be the expected total amount raised for the charity (including the dinner ticket profits and spontaneous donations)?

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 50% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 30%of the time on airline #3. For airline #1, flights are late into D.C. 15% of the time and late into L.A. 10% of the time. For airline #2, these percentages are 40% and 30%, whereas for airline #3 the percentages are 35% and 20%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.)