Concept explainers
A
Interpretation: The combination of courses that minimize the total cost of books is to be proposed.
Concept Introduction: A business student requires completing 65 courses to attain graduation. While the business courses should be greater than or equal to 23, the non-business should be greater than or equal to 20. While an average business course needs a textbook that costs $60 and 120 hours of study; the non-business courses require a textbook that costs $24 and 200 hours of study.
B
Interpretation: The surplus or stock variables, based on the given data should e determined.
Concept Introduction: A business student requires completing 65 courses to attain graduation. While the business courses should be greater than or equal to 23, the non-business should be greater than or equal to 20. While an average business course needs a textbook that costs $60 and 120 hours of study; the non-business courses require a textbook that costs $24 and 200 hours of study.
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Operations Management: Processes and Supply Chains (12th Edition) (What's New in Operations Management)
- 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.arrow_forwardThe 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.)arrow_forwardThe 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?arrow_forward
- 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%.arrow_forwardLemingtons 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?arrow_forwardSIMPLEX METHOD A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.arrow_forward
- 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 graphicallyarrow_forwardThe Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend to meet the specifications at minimal cost. How much will the blend cost?Type A Type BShade Tolerance 1 1Traffic Resistance 2 1Drought Resistance 2 5arrow_forwardnJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 same exampe is used but in this case each plant has a different fixed and variable cost structur and cpacity for manufacturing the differnt Juices. the fixed cost only applies if the plant produces any juice Capacity Unit-Month Fixed…arrow_forward
- nJuicy Juice manufactures different juices made entirely of various exotic nuts. Their primary market is China and they operate 3 plants located in Ethiopia, Tanzania and Nigeria. You have been asked to help them determine where to manufacture the two newest juices they offer, Gingko Nut and Kola Nut. Each plant has a different variable cost structure and capacity for manufacturing the different juices. Also each juice has an expected demand. Cost/unit Gingko Kola Ethiopia ¥21.00 ¥22.50 Tanzania ¥22.50 ¥24.50 Nigeria ¥23.00 ¥25.50 Capacity Units/month Ethiopia 425 Tanzania 400 Nigeria 750 Demand Units/month Gingko 550 Kola 450 How much of each juice should be made at each plant in order to minimize total cost while meeting demand and adhering to plant capacity?arrow_forwardUsing Excel Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?arrow_forwardA poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K20 each but young one cost K50 each. The old hens lay 30 eggs per week, and young ones 50 eggs per week, each egg being worth 30ngwee. A hen cost K10 per week to feed. If a person has only K800 to spend on hens, how many of each kind should he buy to get a profit of more than K600 per week assuming that he cannot house more than 200 hens? a) Formulate the problem as a linear programming model b) Using the Big M – method, how many hens should he buy of each kind to maximize the profit per week? c) Identify the binding and non-binding constraints and justify your choicearrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,