1. Philip J. Fry, a managing partner of the investment firm of Fry and Nephews, is designing a portfolio for Hermes Conrad. Conrad has $500,000 cash to invest, and Fry has identified 12 different investments, falling into four broad categories that both Fry and Conrad feel would be potential candidates for the portfolio. In addition, Fry has learned that two investment partnerships will be open to investment six months from now and can be considered to be potential investments at that time.

The tables below list the investments and their important characteristics. The expected annual after-tax returns accounts for all commissions and service charges. Note that Beekman Corporation stock and Beekman Corporation bonds are two separate investments, whereas Calton REIT is a single investment, a stock that is also a real estate investment.

Conrad will hold any money invested in the one-year CD for the entire year. All other investments made at the beginning of the year will be sold at the end of the first six months at which time it is assumed he will have earned 50% of the annual return. The initial amounts in these investments plus the returns will then be available for investments during the second six months. Returns on all investments (except the one-year CD) made during the second six months should again earn 50% of the annual return.

Fry wishes to determine the investments Conrad should make during the first six months of the year and the investments he should make during the second six months of the year that will maximize the total value of the portfolio at the end of the year. However, the investments should be made subject to a number of concerns Conrad has raised regarding his portfolio including:

• Throughout the year the average risk factor must be no greater than 55.
• Throughout the year the average liquidity factor must be at least 85.
• At least $10,000 is to be invested in the Beekman Corporation.
• At least 10% but not more than 50% of the non-"money" portion of the portfolio should be invested in each category of investment during each six-month period.
• With the exception of the money category investments, no more than 20% of the portfolio ($100,000) should be in any one investment.
• At least $25,000 should be kept in the money market fund throughout the year.
• A minimum investment of $125,000 should be in bonds throughout the year.
• Throughout the year at most 40% of the total portfolio in investments with expected annual after-tax returns of less than 10% are to have risk factors exceeding 25.
• Throughout the year at least one-half of the portfolio must be totally liquid (i.e., have a liquidity factor of 100).

Prepare a report to assist Philip J. Fry in developing a portfolio for Hermes Conrad. Include in the report the following analyses:

• The expected after-tax return on the investment plan
• By how much each of Conrad’s restrictions were met, including the determination of the overall risk and liquidity factors
• The expected after-tax return for additional investment above $500,000
• The most sensitive after-tax return estimates that could affect the optimal solution
• The effect of a relaxation in the minimum dollar amount to be placed in the money market fund

Investments Currently Available

Investments Available in Six Months

1. Igor Bender operated a farm under the former Russian collective farm system. The collective farm raised hogs for distribution by the central government as its main activity. Previously, Igor was told how many hogs to raise each year by Moscow’s central planning agency and was allocated the necessary animal feed to raise the hogs. With the new market-driven economy, Igor receives no instructions on how to operate his hog farm and must survive as best as he can on his own by buying animal feed, raising hogs, and selling them to any buyers he can find. Hogs were fed a combination of corn and potatoes, mixed to ensure that minimum amounts of two primary nutrients were met: crude protein and calories. Corn and potato suppliers have become less certain, and Igor has contracted to buy waste food scraps from a nearby food processing plant to supplement the previous hog diet of corn and potatoes. Igor has turned to you, a recently arrived United Nations consultant, for help in managing his farm in the new and very uncertain Russian market economy. On his own, Igor contracted to sell up to 100 hogs to a Moscow butcher in the next month for a fixed price of 450 rubles per hog. In addition, Igor contracted to buy up to 800 kilograms of waste food from the processing plant for a price of 10 rubles per kilogram. He believes he can buy any amount of corn for 19 rubles per kilogram and can purchase up to 600 kilograms of potatoes from a nearby potato farm for 15 rubles per kilogram. The table below presents the monthly requirements per hog in units of protein and thousands of calories, and the supply per kilogram of the same for the three sources of animal feed.

To help Igor understand how to run his farm, build and solve the linear programming problem, perform sensitivity analysis, and present him with a report. In particular be sure to answer the following questions which were posed to you by Igor in a recent conversation:

• How much money can I make from this farm? How many hogs will I sell, and how much corn, potatoes, and food scraps should I buy now?
• I think I can persuade the butcher to buy another 5 hogs from me at the same 450 ruble price. Would it improve my situation?
• Everything is very volatile now. For example, it could easily happen that the cost of the corn might suddenly change. How would such a change affect my plans?
• Business relationships are really uncertain in Russia just now. I am nervous that the farm manager selling me the potatoes will not honor his promise to deliver the 600 kilograms. If he delivers only 500 kilograms of potatoes, how much will I be hurt? What should my new strategy be?
• Are there alternate ways for me achieve the same income involving different operating strategies?
• An international salesman from the Hubert Farnsworth Company stopped by the farm and wants to sell me prepackaged dry hog feed imported from Poland. He wants to charge me 16 rubles per kilogram for the packaged hog food, which includes transportation from Poland. He says each kilogram of his product provides 16 units of crude protein and 150 kilocalories. Should I start importing hog feed from Poland?

1. When John Zoidberg purchased the New New York City Dry Cleaners, he thought that because of its good location near several high-income neighborhoods, he would easily generate business if he improved the building’s physical appearance. Therefore, he invested much his cash reserves in remodeling the exterior and interior of the business. However, he just broke even in the year following his acquisition of the dry cleaners, which he didn’t feel was a sufficient return given how hard he had worked. John didn’t realize that the dry cleaning business is very competitive and success is based more on price and quality service, including quickness of service, than on the building’s appearance.

In order to improve the quality of his service, John is considering purchasing new dry cleaning equipment, including a pressing machine that could substantially increase the speed at which he can dry clean clothes and improve their appearance. The new machinery costs $16,200 installed and can clean 40 clothes items per hour (the shop is open 8 hours a day, 365 days a year). He is considering the financing option offered by the manufacturer, which will allow him to pay off the machine in 36 months at 0% interest. John estimates that he spends $0.25 on supplies per item dry cleaned, which will not change if he purchases the new equipment. His current utility and property tax bills total $1,700 per month. He charges customers $1.10 per clothing item.

1. What is John’s current monthly volume?
2. If John purchases the new equipment, how many additional items will he have to dry clean each month to break even?
3. John estimates that with the new equipment, he can increase his volume to 4,300 items per month. What monthly profit would he realize with that level of business during the next three years? After three years?
4. John believes that if he doesn’t buy the new equipment but lowers his price to $0.99 per item, he will increase his business volume. If he lowers his price, what will his new breakeven volume be? If his price reduction results in a monthly volume of 3,800 items, what will his monthly profit be?
5. John estimates that if he purchases the new equipment and lowers his price to $0.99 per item, his volume will increase to about 4,700 units per month. Because of the local market, that is the largest volume he can realistically expect. What should John do?

1. The workload in many areas of bank operations has the characteristics of a non-uniform distribution with respect to the time of day. For example, at Turanga Leela Bank, the number of domestic money transfer requests received from customers, if plotted against time of day, would appear to have the shape of an inverted U curve, with the peak around 1pm. For efficient use of resources, the personnel available should, therefore, vary accordingly.

A variable capacity can be achieved effectively by employing part-time personnel. Because part-timers are not entitled to all the fringe benefits, they are often more economical than full-time employees. Other considerations, however, may limit the extent to which part-time people can be hired in a given department. The problem is to find an optimum workforce schedule that would meet personnel requirements at any given time and also be economical.

Some of the factors affecting personnel assignments are listed here:

• By corporate policy, part-time personnel hours are limited to a maximum of 40% of the day’s total requirement.
• Full-time employees work for 8 hours (1 hour for lunch included) per day. Thus, a full-timer’s productive time is 35 hours per week.
• Part-timers work for at least 4 hours per day but less than 8 hours and are not allowed a lunch break.
• Fifty percent of the fill-timers go to lunch between 11am and noon, and the remaining 50% go between noon and 1pm.
• The shift starts at 9am and ends at 7pm (i.e., overtime is limited to 2 hours). Any work left over at 7pm is considered hold over for the next day.
• A full-time employee is not allowed to work more than 5 hours of overtime per week. He or she is paid at the normal rate for overtime hours – not at one and one-half times the normal rate applicable to hours in excess of 40 per week. Fringe benefits are not applied to overtime hours.

In addition, the following costs are pertinent:

• The average cost per full-time personnel hour (fringe benefits included) is $10.11.
• The average cost per overtime personnel hour for full-timers (straight rate, excluding fringe benefits) is $8.08.
• The average cost per part-time personnel hour is $7.82.

The personnel hours required, by hour of day, are given in the table below. The bank’s goal is to achieve the minimum possible personnel cost subject to meeting or exceeding the hourly workforce requirements as well as the constraints on the workers listed earlier. Prepare a report to the bank manager proposing a solution.

1. Amy Wong is packing for a trip and is considering fifteen items. Their values for the trip and weights are shown in the following table. The maximum weight she can carry is 15 pounds. In addition, there must be at least one food item and she may take either the camera or the radio but not both. How should Amy pack her bag?

Price: $35.15

Solution: The downloadable solution consists of 12 pages, 2315 words and 2 charts.
Deliverable: Word Document