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t 1 t ,_ y e Questions and Problems 1 Z9 five years from now. The Merrits estimate that her first year college expenses will amount to $12,000 and increase $2,000 per year during each of the remaining three years of her education. The following investments are available to the Merrits: Investment Available Matures Return at Maturity A Every year 1 year 6% B 1,3,5, 7 2 years 14% c 1, 4 3 years 18% D 1 7 years 65% The Merrits want to determine an investment plan that will provide the necessary funds to cover Lisa's anticipated college expenses with the smallest initial invest-ment. a. Formulate an LP model for this problem. b. Create a spreadsheet model for this problem, and solve it using Solver. c. What is the optimal solution? 43. Refer to the previous question. Suppose the investments available to the Merrits have the following levels of risk associated with them. Investment Risk Factor A 1 B 3 c 6 D 8 If the Merrits want the weighted average risk level of their investments to not exceed 4, how much money will they need to set aside for Lisa's education, and how should they invest it? a. Formulate an LP model for this problem. b. Create a spreadsheet model for this problem, and solve it using Solver. c. What is the optimal solution? 44. A natural gas trading company wants to develop an optimal trading plan for the next 10 days. The following table summarizes the estimated prices per thousand cubic feet (cf) at which the company can buy and sell natural gas during this time. The company may buy gas at the" Ask" price and sell gas at the "Bid" price. Day Bid Ask I 2 $3.06 $4.01 $3.22 $4.10 3 $6.03 $6.13 4 $4.06 $4.19 5 $4.01 $4.05 6 $5.02 $5.12 7 $5.10 $5.28 8 $4.08 $4.23 9 10 $3.01 $4.01 $3.15 $4.18 The company currently has 150,000 cf of gas in storage and has a maximum storage capacity of 300,000 cf. To maintain the required pressure in the gas transmission pipeline system, the company can inject no more than 200,000 cf into the storage fa-cility each day and can extract no more than 180,000 cf per day. Assume extractions occur in the morning and injections occur in the evening. The owner of the storage facility charges a storage fee of 5% of the market (bid) value of the average daily gas inventory. (The average daily inventory is computed as the average of each day's beginning and ending inventory.) a. Create a spreadsheet model for this problem and solve it. b. What is the optimal solution? c. Assuming price forecasts for natural gas change on a daily basis, how would you suggest the company in this problem actually use your model? ' .~ l ' '

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