The Pyrotec Company produces three electrical productsclocks, radios, and toasters. These products have the following resource requirements: Resource Requirements Cost/Unit Labor Hours/Unit Clock $7 2 Radio 10 3 Toaster 5 2 The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12. The company wants to know the optimal product mix that will maximize profit. a. Formulate a linear programming model for this problem. b. Solve the model by using the computer.
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The Pyrotec Company produces three electrical productsclocks, radios, and toasters. These products have the following resource requirements:
Resource Requirements
Cost/Unit Labor Hours/Unit
Clock $7 2
Radio 10 3
Toaster 5 2
The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200
clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12. The company wants to know the optimal product mix
that will maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
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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?
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Linear Programming Problem The Pyrotec Company produces three small kitchen appliances – waffle makers, egg cookers, and toasters. The three products have the following requirements: Resource Requirements Metal Materials/unit Plastic Materials /unit Labor hours/unit Waffle maker 3.1 lb 0.5 lb .7 Egg cooker 1.5 lb 0.7 lb 1 Toaster 2.0 lb 0.3 lb .5 Resource costs are $3 per pound of metal, $2.90 per pound of plastic and $10.00 per hour for labor. Available resources are 200 pounds of metal, 250 pounds of plastic and 350 hours of labor. Based on market research, the company expects the maximum demand for waffle makers is 50 and for egg cookers is 75. The company has a contract to supply 25 toasters to a local department store. Waffle makers will be sold for 24.99, egg cookers will be sold for 19.99 and Toasters will sell for 14.99 The company wants to know the optimal product mix that will maximize profit. Part A. Write the…The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of P350 each, and tables will result a profit of P1,000 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? What is the largest profit? Use the graphical LP approach. (First construct a table of resource requirements and profit).
- A large business process outsourcing company operates 5 days a week (Monday to Friday). The manager estimates that the minimum number of agents requires, a combined on-site and work-from-home (WFH) setup, to provide prompt service: 20 for Monday, 18 for Tuesday, 23 for Wednesday, 28 for Thursday, and 32 for Friday. Labor rules state that each agent must work for 3 days a week on-site. and 2 days in WFH setup. For example. an agent who works on-site Monday to Wednesday must be on WFH setup during Thursday and Friday. Also. the company wants at least 60% of the workforce daily to report on-site. Formulate the appropriate LP model for this problem to minimize the number of agents to be hired.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.…Celestial Artistry Company is developing departmental overhead rates based on direct-labor hours for its two production departments, Etching and Finishing. The Etching Department employs 20 people and the Finishing Department employs 80 people. Each person in these two departments works 2,000 hours per year. The production-related overhead costs for the Etching Department are budgeted at $200,000, and the Finishing Department costs are budgeted at $320,000. Two service departments, Maintenance and Computing directly support the two production departments. These service departments have budgeted costs of $48,000 and $250,000, respectively. The production departments’ overhead rates cannot be determined until the service departments’ costs are allocated. The following schedule reflects the use of the Maintenance Department’s and Computing Department’s output by the various departments. Using Department Service Department Maintenance Computing Etching Finishing Maintenance (maintenance…
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