The production planning period for flat-screen monitorsat Louisiana's Rao Electronics, Inc., is 4 months. Cost dataare as follows: CEO Mohan Rao expects to enter the planning period with 500monitors in stock. Backordering is not permitted (meaning, forexample, that monitors produced in the second month cannot beused to cover first month's demand). Develop a production planthat minimizes costs using the transportation method. Regular-time cost per monitor$ 70Overtime cost per monitor$110Subcontract cost per monitorialCarrying cost per monitor per monthd h t r $120$ 4For each of the next 4 months, capacity and demand for flat-screen monitors are as follows:PERIODMONTH 1 MONTH 2 MONTH 3"MONTH4DemandСараcityRegular timeOvertimeSubcontract2,0002,5001,5002,1001,5004007501,6001,600400600200400600600600"Factory closes for 2 weeks of vacation.

A Small Introduction about Transportation Transportation is an initial course intended to assist…

Regular-time cost per monitor $ 70 Overtime cost per monitor $110 Subcontract cost per monitorial Carrying cost per monitor per month d h t r $120 $ 4 For each of the next 4 months, capacity and demand for flat- screen monitors are as follows: PERIOD MONTH 1 MONTH 2 MONTH 3" MONTH 4 Demand Сараcity Regular time Overtime Subcontract 2,000 2,500 1,500 2,100 1,500 400 750 1,600 1,600 400 600 200 400 600 600 600 "Factory closes for 2 weeks of vacation.

Regular-time cost per monitor $ 70 Overtime cost per monitor $110 Subcontract cost per monitorial Carrying cost per monitor per month d h t r $120 $ 4 For each of the next 4 months, capacity and demand for flat- screen monitors are as follows: PERIOD MONTH 1 MONTH 2 MONTH 3" MONTH 4 Demand Сараcity Regular time Overtime Subcontract 2,000 2,500 1,500 2,100 1,500 400 750 1,600 1,600 400 600 200 400 600 600 600 "Factory closes for 2 weeks of vacation.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 73P

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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?
Don't use chatgpt, I will 5 upvotes Alan wants to bake blueberry muffins and bran muffins for the school bake sale. For a tray of blueberry muffins, Alan uses 1/3 cup of oil and 2 eggs. For a tray of bran muffins, Alan uses 1/2 cup of oil and 1 egg. Alan has 4 cups of oil and 12 eggs on hand. He sells trays of blueberry muffins for $12 each and trays of bran muffins for $9 each. Alan wants to maximize the money raised at the bake sale. Let x represent the number of blueberry muffins and y represent the number of bran muffins Alan bakes.
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 $250. Radios made during a month may be used to meet demandfor that month or any future month. Assume that productionduring each month must be a multiple of 100. Given thatthe initial inventory level is 0 units, use dynamicprogramming to determine an optimal production schedule.
You own wheat warehouse with capacity of 20,000 bushels. At the beginning of month 1, you have 6,000 bushels of wheat. Each month, wheat can be bought and sold at the price per 1000 bushels given in the table Month Selling price ($) Purchase prie ($) 1 3 8 2 6 8 3 7 2 4 1 3 5 4 4 6 5 3 7 5 3 8 1 2 9 3 5 10 2 5 The sequence of events during each month is as follows: a. You observe your initial stock of wheat. b. You can sell any amount of wheat up to your initial stock at the current month's selling price. c. You can buy(at the current month's buying price) as much wheat as you want, subject to the warehouse size imitation. Your goal is to formulate an LP that can be used to determine how to maximise the profit earned over the next 10 months and solve using Excel solver or AMPL
1) The Sanders Garden Shop sells two types of grass seeds. Each type of grass seed needs different resources (per pound) as shown in table. Type Basic seeds provides a profit of $3 and Type Super provides a profit of $4.5 per pound. Type Basic Type Super Area in square feet 1 1 Pesticides 2 1 Harvesting &Packaging hours 2 5 Let X = the pounds of Type Basic seed Let Y= the pounds of Type Super seed The Linear Program has been provided as follows: Max 3X + 4.5Y s.t. 1A + 1B ≤ 300 ------1 2A + 1B ≤ 400 -------2 2A + 5B ≤ 750 --------3 A , B ≥ 0 USE GRAPHICAL SOLUTION PROCEDURE TO SOLVE THE LINEAR PROGRAM AND PERFORM THE FOLLOWING STEPS. • Draw the constraints • Shade the feasible region • Corners should be clear and make an arrow to define the feasible region. .Point out the optimal corner on the graph ( the…
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:i. Compute the value of the objective function…
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3. A ton of solvent base is a mixture of 1/2 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced.RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:Raw Material Amount Available for ProductionMaterial 1 20 tonsMaterial 2 5 tonsMaterial 3 21 tonsAssuming that RMC is interested in maximizing the total profit contribution, answer the following:a. What is the linear programming model for this…
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