Consider the information below for THREE questions.Modify the employee scheduling model in class so that each worker works 10 hours a dayin four consecutive days and then rest for three days in any 7-day cycle. Employees are paid$10 per hour on weekdays and $12 per hour on weekends. Change the objective so thatyou now minimize the weekly payroll. Use the the following spreadsheet output (screenshotwith purposely hidden information) to answer the questions.C9 Wed10 Thu11 Fri12 Sat13 SunA1 Employee scheduling model2 Hourly wage rates3 Weekday$104 WeekendS Hours per day$12106 Decision variables: number of employees starting their four-day shift on various days7 Mon8 Tue26 Employees required27B17 Tue18 Wed19 Thị20 Fri21 Sat22 Sun23 Constraint on employee availabilities24 Employees available172528 Objective to minimize29 Total employees30 Weekly payrollO 11620O 12150.O 1320074414 Result of decisions: number of employees working on various days (along top) who started their shift on various days (alongside)15Mon Tue WedThuFriSatSun16 MonO 1182017D1313S17151919XG1514X18H16Y13Q: Given the current values for the decision variables, what's the value in cellB30 which represents the weekly payroll?11

Linear programming is a mathematical technique that is also used in operations management…

Answered: Q: Given the current values for the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 67P

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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?
A company must meet (on time) the following demands:quarter 1—30 units; quarter 2—20 units; quarter 3—40units. Each quarter, up to 27 units can be produced withregular-time labor, at a cost of $40 per unit. During eachquarter, an unlimited number of units can be produced withovertime labor, at a cost of $60 per unit. Of all unitsproduced, 20% are unsuitable and cannot be used to meetdemand. Also, at the end of each quarter, 10% of all unitson hand spoil and cannot be used to meet any futuredemands. After each quarter’s demand is satisfied andspoilage is accounted for, a cost of $15 per unit is assessedagainst the quarter’s ending inventory. Formulate an LP thatcan be used to minimize the total cost of meeting the nextthree quarters’ demands. Assume that 20 usable units areavailable at the beginning of quarter 1.
How much influence can the employee requirements for one, two, or three days have on the weekly schedule in the employee scheduling example? Explore this in the following questions: a. Let Monday’s requirements change from 17 to 25 in increments of 1. UseSolverTable to see how the total number of employees changes.b. Suppose the Monday and Tuesday requirements can each, independently of one another, increase from 1 to 8 in increments of 1. Use a two-way SolverTable to see how the total number of -employees changes.c. Suppose the Monday, Tuesday, and Wednesday -requirements each increase by the same amount, where this increase can be from 1 to 8 in -increments of 1. Use a one-way SolverTable to -investigate how the total number of employees changes.
A manufacturing process has 12 workers and 6 stations. The process iscompleted in the order given below. Where there are multiple workers within a station,each worker works independently on his/her own unit. Assume inventory buffers areallowed between each station.Station Staffing Processing time (hoursper unit per worker)A 2 2.20B 1 1.25C 3 2.00D 2 2.60E 3 3.00F 1 0.75What is the maximum number of units per hour that can be produced? Assume they startthe day with inventory at each station to work on
Based on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run theday shift and $6000 to run the night shift. Demand for the next two days is as follows: day 1, 4000; night 1, 3000; day 2, 2000; night 2, 5000. It costs $1 per unit to hold a unit in inventory for a shift.a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.)b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventorylevel. Is this…
Please note that this question is different from what you have in your library. This question has 3 variables ie 3 departments. Please help solve the problem. A co markets 2 products which are produced in 3 successive departments. The contribution per unit of the 2 products and the production capacity of the 3 departments are X. Y Contribution. 10. 15 Machining dept (hrs) 3. 4 Foundry dept (hrs) 4 2 Painting dept (hrs) 4 5 A constraint on production is that each dept has a limited number of hours available for the forthcoming plan period as shown below: Department. Available hours Machining. 1'200 Foundry. 1000 Painting. 1300 Required- 1. Formulate the linearr programming problem for the above information. 2. Solve them graphically
Based on Zangwill (1992). Murray Manufacturingruns a day shift and a night shift. Regardless of thenumber of units produced, the only production costduring a shift is a setup cost. It costs $8000 to run theday shift and $4500 to run the night shift. Demand forthe next two days is as follows: day 1, 2000; night 1,3000; day 2, 2000; night 2, 3000. It costs $1 per unitto hold a unit in inventory for a shift.a. Determine a production schedule that minimizesthe sum of setup and inventory costs. All demandmust be met on time. (Note: Not all shifts have tobe run.)b. After listening to a seminar on the virtues of theJapanese theory of production, Murray has cut thesetup cost of its day shift to $1000 per shift and thesetup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes thesum of setup and inventory costs. All demand mustbe met on time. Show that the decrease in setupcosts has actually raised the average inventorylevel. Is this reasonable?
An electronics firm has a contract to deliver thefollowing number of radios during the next three months;month 1, 200 radios; month 2, 300 radios; month 3, 300radios. For each radio produced during months 1 and 2, a$10 variable cost is incurred; for each radio produced duringmonth 3, a $12 variable cost is incurred. The inventory costis $1.50 for each radio in stock at the end of a month. Thecost of setting up for production during a month is $250. Radios made during a month may be used to meet demandfor that month or any future month. Assume that productionduring each month must be a multiple of 100. Given thatthe initial inventory level is 0 units, use dynamicprogramming to determine an optimal production schedule.
Please complete all work in excel. Use excel to make any necessary calculations and be sure to identify the answer, including units (if necessary). Answers that need formulas must have them within the answer cell. City wants to further develop the model to include the weather conditions of rainy, cloudy, or sunny. Pool Attendance Temperature (°F) Weather Condition 150 89 Sunny 100 82 Rainy 125 81 Cloudy 130 86 Cloudy 155 93 Cloudy 170 98 Sunny 200 99 Sunny 180 87 Sunny 190 88 Sunny 140 83 Sunny 120 82 Cloudy 90 81 Rainy 130 87 Rainy 120 93 Rainy Should you keep weather condition in the model?
A total of 160 hours of labor are available each week at$15/hour. Additional labor can be purchased at $25/hour.Capital can be purchased in unlimited quantities at a cost of$5/unit of capital. If K units of capital and L units of laborare available during a week, then L1/2K1/3 machines can beproduced. Each machine sells for $270. How can the firmmaximize its weekly profits?

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Q: Given the current values for the decision variables, what's the value in cell 830 which represents the weekly payroll?