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Textbook Chapter 14, Problem 4. You should answer all parts of the question. I w
Textbook Chapter 14, Problem 4. You should answer all parts of the question. I would like you to use the sensitivity report to answer Parts C and D, specifically. For Part E, you can change the constraint and resolve your model to get the answer. [30 points]
Textbook Chapter 14, Problem 8. [30 points]
Textbook Chapter 14, Problem 17. [20 points]
Textbook Chapter 14, Problem 18. [20 points]
Textbook Chapter 14, Problem 31. [50 points]
Problem 4: Bank Loan Funds Allocation. Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans. LO 1, 2, 3, 5, 6, 7
Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds.
How much should be allocated to each type of loan? What is the total annual return? What is the annual percentage return?
If the interest rate on home loans increases to 9%, would the amount allocated to each type of loan change? Explain.
Suppose the total amount of new funds available is increased by $10,000. What effect would this have on the total annual return? Explain.
Assume that ASB has the original $1 million in new funds available and that the planning committee has agreed to relax the requirement that at least 40% of the new funds must be allocated to home loans by 1%. How much would the annual return change? How much would the annual percentage return change?
Problem 8: Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line of phones. The contract calls for the following Battery Pack Production Quantity
PT-100 200,000
PT-200 100,000
PT-300 150,000
Photon Technologies can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows:
Plant
Product Philippines Mexico
PT-100 0.95 0.98
PT-200 1.34 0.98
PT-300 1.06 1.15
The PT-100 and PT-200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.15 per unit, and the cost of shipping from the Mexico plant is 0.08 per unit.
(a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost associated with the new contract.
(b) Solve the linear program developed in part (a), to determine the optimal production plan. Qty Produced Phillipines Mexico PT-100 16000c 40000 PT-200 100000 0 5000 1000 PT-300 Total Cost-$
(c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-100 in the Philippines plant. If required, round your answer to two decimal digits At least $ / unit.
(d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-200 in the Mexico plant. If required, round your answer to two decimal digits. At least $ .05/ unit.
Problem 17:
The Clark County Sheriff’s Department schedules police officers for 8-hour shifts. The beginning times for the shifts are 8:00 a.m., noon, 4:00 p.m., 8:00 p.m., midnight, and 4:00 a.m. An officer beginning a shift at one of these times works for the next 8 hours. During normal weekday operations, the number of officers needed varies depending on the time of day. The department staffing guidelines require the following minimum number of officers on duty:Time of Day Minimum No. of Officers on Duty
8:00 a.m.–noon 5
Noon–4:00 p.m. 6
4:00 p.m.–8:00 p.m. 7
8:00 p.m.–midnight 7
Midnight–4:00 a.m. 4
4:00 a.m.–8:00 a.m. 6
Determine the number of police officers who should be scheduled to begin the 8-hour shifts at each of the six times to minimize the total number of officers required. (Hint: Let x1 = the number of officers beginning work at 8:00 a.m., x2 = the number of officers beginning work at noon, and so on.) If your answer is zero, enter “0”.
Problem 18:
Bay Oil produces two types of fuels (regular and super) by mixing three ingredients. The major distinguishing feature of the two products is the octane level required. Regular fuel must have a minimum octane level of 90 while super must have a level of at least 100. The cost per barrel, octane levels, and available amounts (in barrels) for the upcoming two-week period are shown in the following table. Likewise, the maximum demand for each end product and the revenue generated per barrel are shown.Input Cost/Barrel Octane Available (barrels)
1 16.5 100 110,000
2 14 87 350,000
3 17.5 110 300,000
Revenue/Barrel Max Demand (barrels)
Regular 18.5 350,000
Super 20 500,000
Develop and solve a linear programming model to maximize contribution to profit
Let Ri = the number of barrels of input i to use to produce Regular, i=1,2,3
Si = the number of barrels of input i use to produce Super, i=1,2,3
What is the optimal contribution to profit?
Max profit = $___ by making ___ barrels of regular ___ and ___ barrels of Super
Problem 31:
Sports of All Sorts produces, distributes, and sells high quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from one of the factories to one of four distribution centers, or DCs, (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U. S. retailers: Just Sports, Sports ‘N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports ‘N Stuff and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping skateboards between the DCs and the retailers. Shipping Costs (per skateboard) Factory to DC Factory/DCs Iowac Maryland Idaho Arkansas Detroit $25.00 $25.00 $35.00 $40.00 Los Angeles $35.00 $45.00 $35.00 $42.50 Austin $40.00 $40.00 $42.50 $32.50 Shipping Costs (per skateboard) DC to Retailer Retailers/DCs Iowa Maryland Idaho Arkansas Just Sports $30.00 $20.00 $35.00 $27.50 Sports ‘N Stuff $27.50 $32.50 $40.00 $25.00 The Sports Dude $30.00 $40.00 $32.50 $42.50
Sports of All Sorts needs to forecast the demand at each of its three retail locations for next year, and then plan how to produce and distribute its product from the factories through the DCs to the retailers. The file skateboards contains five tabs: Plant Capacities, Transportation Costs, DC Capacities, DC Processing Costs, and Historical Demand. LO 1, 2, 3
This exercise assumes knowledge of concepts discussed in Chapter 9.
Construct a scatter plot for the historical demand for each retailer. Use the historical demand to forecast the future demand for each retailer. For Just Sports and Sports ’N Stuff, use the average of the historical demands as the forecast for the next year. For The Sports Dude, use simple linear regression to forecast the demand for the next year. Round your forecast to the nearest one thousand units (e.g., if your forecast is 12,303, round to 12,000 for use in part (b).
Construct a linear programming model of the supply chain.
Solve the linear programming model you constructed in part (b). What is the total cost? Which plants are planned to use all of their capacity? Which distribution centers will use all of their capacity?
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