Instructions:

These problems focus on finding solutions to numerical problems. With that in mind, most problem sets will include a number of problems.

For each problem, you will need to provide more than a simple numerical response.

Your solutions should thoroughly address the issue and present your findings in a meaningful format, similar to those developed within the chapters and as part of the review exercises solutions.

Any Excel spreadsheet models developed to solve the problems should be included with your submission.

Part value may be assigned for incorrect responses.

REFERENCE:

Textbook

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., Cochran, J.J., Fry, M., & Ohlmann, J. (2015). Quantitative methods for business. (13th ed.). Mason, Ohio: Cengage Learning.

CHAPTER 8

2g. The Pfeiffer Company manages approximately $15 million for clients_ For each client, Pfeiffer chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund. Each client has different investment objectives and different tolerances for risk. To accomm.udate the differences, Pfeiffer places limits on the per¬centage of each portfolio that may be invested in the three funds and assigns a portfolio risk index to each client.

Here's how the system works for Dennis Hartrnan.n.. one of Pfeiffer's clients.. Based on an evaluation of Hartmann's risk tolerance, Pfeiffer has assigned Hartinann's portfolio a risk index of 0.05. Furthermore, to maintain diversity, the fraction of Hartrnann's portfolio invested in the growth and income funds must be at least ID% for each, and at least 20% must be in the money market fund.
The risk ratings for the growth, income, and money market funds arc 0.10, 0.05, and 0.01. respectively. A portfolio risk index is computed as a weighted average of the risk ratings for the three funds, where the weights are the fraction orate portfolio invested in each of the funds. Hartmann has given Pfeiffer 5300,000 to manage. Pfeiffer is currently forecasting a yield of 2E)% on the growth fund.. 10% on the income fund, and 6% on the money market furry

a. Develop a linear programming model to select the best mix of investments fur Hartman.n's portfolio.

b. Solve the model you developed in part (a).

c. How much may the yields on the three funds vary before it will be necessary for Pfeiffer- to modify Hartmann "s portfolio?

d. If Hartmann were more risk tolerant, how much or a yield inc....rea_sc could he expect? For instance, what if his portfolio risk index is increased to 0.06?

c. If Pfeifferrevised the yield estimate for the growth fund downward to 0.10, how would you recommend modifying Hartmann's portfolio?
What information must Pfeiffer maintain on each client in order to use this system to manage client portfolios?

g. On a weekly basis Pfeiffer revises the yield estimates for the three funds.. Suppose Pfeiffer has 50 clients.. Describe how you would envision Pfeiffer making weekly modifications in each client's portfolio and allocating the total funds managed anaorig the three investment funds.

CHAPTER 9

The management of !Unman Company is tryin.g to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:

a. Develop a linear programming model of the Hartman Company problem. Solve the model to determine the optimal production quantities of products 1 and I

b. In computing the profit contribution per unit, management doesn't deduct labor costs because they arc considered Fixed for the upcoming planning. period_ However, N up¬post,t that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime.? How much would you be willing to pay per hour of overtime in each department?

c. Suppose that 10., 6, and 8 hours of overtime may be scheduled in departments A, B. and C. rcspc-ctivciy. 11-ie cost pcf hour or ovcrtinv i$ Sig in departirnent A, 522.50 in de¬partment B. and $12 in department C. Formulate a linear programming model that can be ustd to determine the optimal production quantities if overtime is made available. Vifrhat arc the optimal production quantities, and what is the n:vised total contribution. to profit? HOW much overtime do you recommend using in each department? What is the increase. in the total contribution to profit if overtime is used?

18. The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck. The company recently contracted to supply gasoline distributors in southern Ohio, and it has S1500,000 available to spend on the rtccc sar expartsion of its Met of gasoline tank trucks.

Thrce models of gasoline tank trucks are available.

The company estimates that the monthly demand for the region will be 550,000 gallons of gasoline. Because of the size and speed differences of the trucks, the number of de¬liveries or round trips possible per month for each truck model will vary. Trip capacities are estimated at 15 trips per month for the Super Tanker, 20 trips per -month for the Regular Line. and 25 tripN per month for the Econo-Tanker. Based on ntaintenantx and driver availability, the firm does not want to add more than 15 new vehicles to its fleet. In addition, the company has decided to purchase at least three of the new Econo-Tankers for usc on sbort-run, low-demand routes. As a fmai constraint, the company does not want more than half the new models to be Super Tankers.

a, if the company wishes to satisfy the gasoline demand with a minimum monthly oper¬ating expense, how many models of each truck should be purchased?

If the company did AM require at least three: Sono-Tankers and did not limit the number of Super Tankers to at most half the new models, how many models of each truck should be purchased'?

2 Star Powes Company is a power company in the. Midiavest region of the United State_ S tar buys and sells energy on the spot market Star can store power in a high-capacity battery that can store up to 60 kWh (kilowatt hours)= During a panic !Aar period. Star can buy or sell electricity at the market price known as LMP (Locational Marginal Prim:). The maximum rate that power can be injected or withdrawn from the battery is 20 kWh per period. Star has forecastcd the following L'MPs for the next 10 periods:

The baltery is full at the beginning of period 1; that us, at the start of the planning horizon, the battery contains 60 kWh of electricity.
Develop a linear programming model Star Power can use to determine when to buy and sell electricity in order to maximize profit over these 10 weeks. What is the maxi-mum achievable profit?

b. Your solution to purl (a) should result in a battery level of D at the end of period 10. Why does this make sense? Modify your mr.xlel with the ratuirement that the battery should be fuill (60 kWh.) at the end %Al-period 10. How does this impact the optimal profit?

c. To further investigate the impact of requirements on the trattery level at the end of period 10, solve your model from part (b) with the constraint on the ending battery level varying from ll kWh to 60 kWh in increments of 10 kWh. Develop a graphl,vith profit on the vertical axis and required ending battery level on the horizontal axis_ Given that Star has not forecasted Lei Ps for periods 1 1.. 12, and so on, what ending battery level do you recommend that Star use in its optimization model?

CHAPTER 10

Tri-County Utilities. Inc- supplies natural gas to customers in a three-county tea. Thecompany purchases natural gas from two coinpanis: So-Ahern Gas and Northwest Gas_ Demand forecasts for the cornin.g winter season am as follows: Hamilton County, 400 units; Butler County, 200 and Clc_Trnont C01111 ly, 311X..11 units.. Contracts to provide the following quantitim have boon written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary.. depending upon the location of the suppliers_ The distribution costs per unit (in thousands of dollars) arc as follows:

From                        Iiiimilten                 Butler                    Clermont

Southern Gas           10                               20                          15

Northwest Gas         12                              15                          18

a. Develop a network mpresentation of this problem.

b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.

c. Dcseribe the distribution plan and show the total distribution cost,

d. Recent resicktntial and industrial growth in Butler County has the potential for increas¬ing demand by as much a S. I 00 units. Which supplier should Tri-County contract with to supply the addiLional capacity'?

7. Aggie Power Genenition supplies electrival power to residential eustomfazi fir many U.S. (Talcs. Its main power generation plants are lecatod in Los Angeles, Tulsa. and Seattle. The following table shows Aggie Power Generation's major residential markets,. the annual demand in each rime/0a (in megawatts or MW),. and the cost to supply electricity Cu each market from each power generation plant (prices are in Sn'AW).

a. Tr there arc no retrii,:tions; on the =aunt of power that can be supplied by any of the power plants. what the optimal solution to this problem? Which cities Khould be sleppciod by which power plants? What is. the total annual power distribution cost for this solution?

b. If at most 40010 MW of power can be supplied by any one of the power plants+ what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation?