## 24 Feb A linear programming computer package is needed.Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. On

A linear programming computer package is needed.Frandec Company manufactures, assembles, and rebuilds material-handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec's production schedule calls for 4,500 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.ComponentManufacturing CostPurchase CostFrame$37.00$50.00Support$10.50$14.00Strap$5.50$6.50Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.ComponentDepartmentCuttingMillingShapingFrame3.52.23.1Support1.31.72.6Strap0.8—1.7Capacity (hours)350420680(a)Formulate and solve a linear programming model for this make-or-buy application. (Let *FM* = number of frames manufactured, *FP* = number of frames purchased, *SM* = number of supports manufactured, *SP* = number of supports purchased, *TM* = number of straps manufactured, and *TP* = number of straps purchased. Express time in minutes per unit.)Min Cutting constraint Milling constraint Shaping constraint Frame constraint Support constraint Strap constraint *FM*, *FP*, *SM*, *SP*, *TM*, *TP* ≥ 0How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number.)(*FM*, *FP*, *SM*, *SP*, *TM*, *TP*) = (b)What is the total cost (in $) of the manufacturing and purchasing plan?$ (c)How many hours of production time are used in each department? (Round your answers to two decimal places.)Cutting hrsMilling hrsShaping hrs(d)How much (in $) should Frandec be willing to pay for an additional hour of time in the shaping department?$ (e)Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec improve its position by pursuing this opportunity? Why or why not? (Round your answer to three decimal places.) —Select— Yes No . The reduced cost of indicates that the solution —Select— can cannot be improved.

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**[–/20 Points]DETAILSASWMSCI15 4.E.019.MY NOTESASK YOUR TEACHER**A linear programming computer package is needed.The Silver Star Bicycle Company will be manufacturing both men's and women's models for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown.ModelProduction CostsLabor Requirements (hours)Current InventoryManufacturingAssemblyMen's$1202.01.520Women's$901.61.030Last month the company used a total of 1,000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. Only integer amounts of bicycles can be produced.(a)Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements.men's model in month 1 bicycleswomen's model in month 1 bicyclesmen's model in month 2 bicycleswomen's model in month 2 bicyclesTotal Cost$ What inventories will be maintained?Inventory Schedulemen's model in month 1 bicycleswomen's model in month 1 bicyclesmen's model in month 2 bicycleswomen's model in month 2 bicyclesWhat are the monthly labor requirements?previous month hrsmonth 1 hrsmonth 2 hrs(b)If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule?men's model in month 1 bicycleswomen's model in month 1 bicyclesmen's model in month 2 bicycleswomen's model in month 2 bicyclesTotal Cost$ How much will the cost increase?$

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**[20/20 Points]DETAILSPREVIOUS ANSWERSCAMMIMS16 4.E.021.MY NOTESASK YOUR TEACHER**A linear programming computer package is needed.Greenville Cabinets received a contract to produce cabinets for a major furniture distributor. The contract calls for the production of 3,300 small cabinets and 4,100 large over the next two months, with the following delivery scheduleModelMonth 1Month 2Small2,1001,200Large1,5002,600Greenville estimates that the production time for each small cabinet is 0.7 hours and the production time for each large cabinet is 1 hour. The raw material costs are $10 for each small cabinet and $12 for each large cabinet. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2,400 hours of regular production time available each month and up to 1,000 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. (Round your answers to the nearest integer. Let SaR = regular small cabinets for month 1, SbR = regular small cabinets for month 2, LaR = regular large cabinets for month 1, LbR = regular large cabinets for month 2, SaO = overtime small cabinets for month 1, SbO = overtime small cabinets for month 2, LaO = overtime large cabinets for month 1, and LbO = overtime large cabinets for month 2)(SaR, SbR, LaR, LbR, SaO, SbO, LaO, LbO)= 2100, 1200, 930, 1560, 0, 0, 610, 1000 Total Production Cost=$

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**[3.99/20 Points]DETAILSPREVIOUS ANSWERSCAMMIMS16 4.E.023.MY NOTESASK YOUR TEACHER**A linear programming computer package is needed.EZ-Windows, Inc., manufactures replacement windows for the home remodeling business. In January, the company produced 15,000 windows and ended the month with 9,000 windows in inventory. EZ-Windows' management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown, the management team does not think a smooth production schedule with the same production quantity each month possible.FebruaryMarchAprilSales forecast15,00016,50020,000Production capacity14,00014,00018,000Storage capacity6,0006,0006,000The company's cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate a linear programming model that will minimize the cost (in dollars) of changing production levels while still satisfying the monthly sales forecasts. (Let *F* = number of windows manufactured in February, *M* = number of windows manufactured in March, *A* = number of windows manufactured in April, *I*1 = increase in production level necessary during month 1, *I*2 = increase in production level necessary during month 2, *I*3 = increase in production level necessary during month 3, *D*1 = decrease in production level necessary during month 1, *D*2 = decrease in production level necessary during month 2, *D*3 = decrease in production level necessary during month 3, *s*1 = ending inventory in month 1, *s*2 = ending inventory in month 2, and *s*3 = ending inventory in month 3.)Min *z*=1*iƒ*+1*Im*+1*Ia*+0.65*Dƒ*+0.65*Dm*+0.65*Da*

Your answer(s) should be in the form of expression(s).s.t.February Demand9000+*F*−15000+*Sƒ*

Enter an equation.March Demand*Sƒ*+*M*−16500=*Sm*

Check which variable(s) should be in your answer.April Demand*Sm*+*A*−20000=*Sa*

Check which variable(s) should be in your answer.Change in February Production*F*−15000=*Iƒ*−*Dƒ*

Check which variable(s) should be in your answer.Change in March Production*M*−*F*=*Im*−*Dm*

Check which variable(s) should be in your answer.Change in April Production*A*−*M*=*Ia*−*Da*

Check which variable(s) should be in your answer.February Production Capacity*F*≤14000 March Production Capacity*M*≤14000 April Production Capacity*A*≤18000 February Storage Capacity*Sƒ*≤6000

Check which variable(s) should be in your answer.March Storage Capacity*Sm*≤6000

Check which variable(s) should be in your answer.April Storage Capacity*Sa*≤6000

Check which variable(s) should be in your answer.Find the optimal solution.(*F*, *M*, *A*, *I*1, *I*2, *I*3, *D*1, *D*2, *D*3, *s*1, *s*2, *s*3) = Cost = $

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**[–/20 Points]DETAILSCAMMIMS16 4.E.025.MY NOTESASK YOUR TEACHER**A linear programming computer package is needed.Western Family Steakhouse offers a variety of low-cost meals and quick service. Other than management, the steakhouse operates with two full-time employees who work 8 hours per day. The rest of the employees are part-time employees who are scheduled for 4-hour shifts during peak meal times. On Saturdays the steakhouse is open from 11:00 a.m. to 10:00 p.m. Management wants to develop a schedule for part-time employees that will minimize labor costs and still provide excellent customer service. The average wage rate for the part-time employees is $7.60 per hour. The total number of full-time and part-time employees needed varies with the time of day as shown.TimeNumber of Employees Needed11:00 a.m.–Noon9Noon–1:00 p.m.91:00 p.m.–2:00 p.m.92:00 p.m.–3:00 p.m.33:00 p.m.–4:00 p.m.34:00 p.m.–5:00 p.m.35:00 p.m.–6:00 p.m.66:00 p.m.–7:00 p.m.127:00 p.m.–8:00 p.m.128:00 p.m.–9:00 p.m.79:00 p.m.–10:00 p.m.7One full-time employee comes on duty at 11:00 a.m., works 4 hours, takes an hour off, and returns for another 4 hours. The other full-time employee comes to work at 1:00 p.m. and works the same 4-hours-on, 1-hour-off, 4-hours-on pattern.(a)Develop a minimum-cost schedule for part-time employees. (Let *xi* = the number of part-time employees who start work beginning at hour *i* where *i* = 1 = 11:00 a.m., *i* = 2 = Noon, etc).Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. *x*1, *x*2, *x*3, *x*4, *x*5, *x*6, *x*7, *x*8 ≥ 0Find the optimal solution.(*x*1, *x*2, *x*3, *x*4, *x*5, *x*6, *x*7, *x*8) = (b)What is the total payroll (in $) for the part-time employees?$ How many part-time shifts are needed? shiftsUse the surplus variables to comment on the desirability of scheduling at least some of the part-time employees for 3-hour shifts.

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(c)Assume that part-time employees can be assigned either a 3-hour or a 4-hour shift. Develop a minimum-cost schedule for the part-time employees. (Let *xi* be the same variables from part a. Let *yi* = the number of part-time employees who start work beginning at hour *i* where *i* = 1 = 11:00 a.m., *i* = 2 = Noon, etc).Min s.t.11:00 a.m. Noon 1:00 p.m. 2:00 p.m. 3:00 p.m. 4:00 p.m. 5:00 p.m. 6:00 p.m. 7:00 p.m. 8:00 p.m. 9:00 p.m. *x*1, *x*2, *x*3, *x*4, *x*5, *x*6, *x*7, *x*8, *y*1, *y*2, *y*3, *y*4, *y*5, *y*6, *y*7, *y*8, *y*9 ≥ 0Find the optimal solution.(*x*1, *x*2, *x*3, *x*4, *x*5, *x*6, *x*7, *x*8, *y*1, *y*2, *y*3, *y*4, *y*5, *y*6, *y*7, *y*8, *y*9) = How many part-time shifts are needed, and what is the cost savings (in $) compared to the previous schedule?part-time shifts neededcost savings$

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