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Information on a prospective investment for Wells Financial Services is given below. Period 1 3000 4500 100 3 4000 4 5000 110% Loan Funds Available...

Question 1-6
1. Information on a prospective investment for Wells Financial Services is given below. Period 1 2 3 4 Loan Funds Available 3000 7000 4000 5000 Investment Income (% of previous period’s investment) 110% 112% 113% Maximum Investment 4500 8000 6000 7500 Payroll Payment 100 120 150 100 In each period, funds available for investment come from two sources: loan funds and income from the previous period's investment. Expenses, or cash outflows, in each period must include repayment of the previous period's loan plus 8.5% interest, and the current payroll payment. In addition, to end the planning horizon, investment income from period 4 (at 110% of the investment) must be sufficient to cover the loan plus interest from period 4. The difference in these two quantities represents net income, and is to be maximized. How much should be borrowed and how much should be invested each period? 2. A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor’s estimate of the time, in days, is given in the table below. Use the computer solution to see which team works with which project. (15 pts) Projects Team Budgeting Informatio n Volunteer s Forecastin g A 32 35 15 27 B 38 40 18 35 C 41 42 25 38 D 45 45 30 42 3. Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk. His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%. Formulate the appropriate linear program. (20 pts) Annual Returns (Planning Scenarios) Mutual Fund Year 1 Year 2 Year 3 Year 4
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International Stock 22.37 26.73 6.46 -3.19 Large-Cap Blend 14.88 18.61 10.52 5.25 Mid-Cap Blend 19.45 18.04 5.91 -1.94 Small-Cap Blend 13.79 11.33 -2.07 6.85 Intermediate Bond 7.29 8.05 9.18 3.92 4. The Super Discount store (open 24 hours a day, every day) sells 8-packs of paper towels, at the rate of approximately 420 packs per week. Because the towels are so bulky, the annual cost to carry them in inventory is estimated at $.50. The cost to place an order for more is $20 and it takes four days for an order to arrive. (5 pts each) a. Find the optimal order quantity. b. What is the reorder point? c. How often should an order be placed? 5. In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions. (2 pts each) a. What is λ ? b. What is μ ? c. Find probability of no units in the system. d. Find average number of units in the system. e. Find average time in the waiting line. f. Find average time in the system. g. Find probability that there is one person waiting. h. Find probability an arrival will have to wait. 6. The medical prognosis for a patient with a certain disease is to recover, to die, to exhibit symptom 1, or to exhibit symptom 2. The matrix of transition probabilities is Recover Die S 1 S 2 Recover 1 0 0 0 Die 0 1 0 0 S 1 1/4 1/4 1/3 1/6 S 2 1/4 1/8 1/8 1/2 a. What are the absorbing states? (4 pts) b. What is the probability that a patient with symptom 2 will recover?(15 pts) End
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