4. The Toones Company has $30,000for the purchase of materials to makethree types of MP3 players. The com-pany has allocated a total of 1200 hoursof assembly time and 180 hours of pack-aging time for the players. The followingtable gives the cost per player, the num-ber of hours per player, and the profit perplayer for each type:Type 1 Type 2 Type 3Cost/$300$300$400PlayerAssembly151510Hours/PlayerPackaging22Hours/PlayerProfit$150$250$200Find the number of players of each typethe company should produce to maxi-mize profit.

Decision variable: Suppose-X be the no. of Type 1 MP3 playerY be the no. of Type 2 MP3 playerZ be…

Answered: 4. The Toones Company has $30,000 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 52P

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If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
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?
4 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.
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.
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…
A gold processor has two (2) sources of gold ore, Source A and source B. To keep his plantrunning, at least three (3) tons of ore must be processed each day. Ore from A costs $20 per tonto process, and ore from B costs $10 per ton to process. Costs must be kept to less than $80 perday. Moreover, Federal Regulations require that number of ore from source B cannot exceedtwice the number of ore from source A. If ore from source A yields 2 oz. of gold per ton, andfrom source B yields 3 oz. of gold per ton, how many tons of ore from both sources must beprocessed each day to maximize the amount of gold to the above constraints?
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?
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 6R + 9C s.t. R + 3 2 C ≤ 1,000 Cutting and sewing 1 2 R + 1 3 C ≤ 300 Finishing 1 8 R + 1 4 C ≤ 100 Packaging and shipping R, C ≥ 0 The computer solution is shown below. Optimal Objective Value = 4350.00000 Variable Value Reduced Cost R 500.00000 0.00000 C 150.00000 0.00000 Constraint Slack/Surplus Dual Value 1 275.00000 0.00000 2 0.00000 4.50000 3 0.00000 30.00000 Variable ObjectiveCoefficient AllowableIncrease AllowableDecrease R 6.00000 7.50000 1.50000 C 9.00000 3.00000 5.00000 Constraint RHSValue AllowableIncrease AllowableDecrease 1 1000.00000 Infinite 275.00000 2 300.00000 100.00000 166.66667 3…

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