The production planning period for flat-screen monitors at Louisiana's Rao Electronics, Inc., is 4 months. Cost data are as follows:Regular-time cost per monitorOvertime cost per monitorSubcontract cost per monitorCarrying cost per monitor per month$70$110$120$4For each of the next 4 months, capacity and demand for flat-screen monitors are as follows:PeriodMonth 3"1,500Month 1Month 22,500Month 4DemandCapacityRegular timeOvertimeSubcontract2,0002,1001,5004006001,6007502006001,600400400600600"Factory closes for 2 weeks of vacation.CEO Mohan Rao expects to enter the planning period with 500 monitors in stock. Backordering is not permitted (meaning, for example, that monitors produced in thesecond month cannot be used in the first month to cover first month's demand).Minimizing total cost using the transportation method, the total cost is $ (enter your response as a whole number).

The transportation problem (TP) is a remarkable kind of Linear Programming problem where the goal is…

Answered: The production planning period for…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section: Chapter Questions

Problem 61P

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Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.
Company Z is contemplating a product development program encompassing 6 major projects. The company is constrained from embarking on all of the projects at once by the number of available (budgeted) developers (60) and the budget allocated for project expenses (£200,000). The following table shows the resource requirements and the estimaled profil for each project. Use EXCEL's Solver to answer question 1 below: 1. What is the maximum profit, and which projects should this company select?
Finco has the following investments available:Investment A For each dollar invested at time 0, we receive $0.10 at time 1 and $1.30 at time 2. (Time 0 =now;time= 1 one year from now; and so on.)Investment B For each dollar invested at time 1, we receive $1.60 at time 2.Investment C For each dollar invested at time 2, we receive $1.20 at time 3.At any time, leftover cash may be invested in T-bills, whichpay 10% per year. At time 0, we have $100. At most, $50can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco’s cash onhand at time 3.
A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…
Formulate an LP model for the following problems.1. Bernadette intends to invest up to ₱50,000 in either Best Fund, or a time deposit orboth. The Best Fund pays 8% per year and the time deposit pays 9%. Because theBest Fund is riskier than the time deposit, so she intends to put at most ₱30,000 intothe time deposit and at least ₱10,000 into the Best Fund. How much should she allotto each investment in order to maximize her returns?
Zucchero Sugar, Inc. has six processing departments for refining sugar—Affination, Carbonation, Decolorization, Boiling, Recovery, and Packaging. Conversion costs are added evenly throughout each process. Data from the month of August for the Recovery Department are as follows: Metric Tons Beginning Work−in−Process Inventory 0 Transferred in 22,000 Ending Work−in−Process Inventory 6,000 Costs Beginning Work−in−Process Inventory $0 Costs added during August : Direct materials 530,000 Direct labor 250,000 Manufacturing overhead 105,000 Total costs added during August $885,000 The ending Work−in−Process Inventory is 100% and 95% complete with respect to direct materials and conversion costs, respectively. The weighted−average method is used. How many metric tons of sugar were refined and transferred to the Packaging Department in August? A. 6,000 metric tons B.…
Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…
KG International produces T-shirts. KG International must decide how many T-shirts to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next three months are 20,000, 32,000, and 30,000. KG International wants to meet these demands on time, knowing that it currently has 5,000 T-shirts in inventory.During each month, there is enough production capacity to produce up to 30,000 T-shirts, and there is enough storage capacity to store up to 10,000 T-shirts after demand has occurred. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.)The forecasted production costs per T-shirt for the next three months are $20, $17, and $22, respectively. The holding cost incurred per T-shirt held in inventory at the end of any month is 10% of the production cost for that month. KG International wants to determine the production schedule that minimizes the total production and…

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