Production & Operations Management
Homework 1 for Section 4
1. 1 Eastman publishing Company is considering publishing a paperback textbook on spreadsheet applications for business. The cost of manuscript preparation, textbook design, and production setup is estimated to be $80,000. Variable production and material costs are estimated to be $3 per book. Demand over the life of the book is estimated to be 4,000 copies. The publisher plans to sell the text to college and university bookstores for $20 each.
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- a. What is the breakeven point?
- b. What pro? Can be anticipated with a demand of 4,000 copies? With a demand of 4,000 copies, what is the minimum price per copy that the publisher must charge to break even?
1. 2 Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket. The rackets are extremely light due to the use of a magnesium-graphite alloy. Each standard-size racket uses 0. 125 kilograms of the alloy and each oversize racket uses 0. 4 kilograms; over the next two-week production period only 80 kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturing time and each oversize racket uses 12 minutes. Also, 40 hours of manufacturing time are available each week. The pro? t contributions are $10 for each standard-size racket and $15 for each oversize racket. How many rackets of each type should CSD manufacture over the next two weeks to maximize the total pro? t contribution?
- a. Decision variables and formulate the problem.
- b. Solve the problem using the graphical method.
1. 3 Management of High Tech Services (HTS) would like to develop a model that will help allocate their technician’s time between service calls to regular contract customers and new customers. A maximum of 80 hours of technician time is available over the two-week planning period. To satisfy cash? ow requirements, at least $800 in revenue (per the technician) must be generated during the two-week period. Technician time for regular customers generates $25 per hour. However, technician time for new customers only generates an average of $8 per hour. To ensure that new customer contracts are being maintained, the technician time spent on new customer contracts must be at least 60% of the time spent on regular customer contracts. Given these 1 revenue and policy requirements, HTS would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contracted during the two-week period will be maximized. Technicians require an average of 50 minutes for each regular customer contract and 1 hour for each new customer contract.
- a. Develop a linear programming model for the problem.
- b. Find the optimal solution via Excel.
1. 4 Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The three graphics designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide a label-designing experience for Sarah, Sarah must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $25 for David, and $18 for Sarah.
- a. Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project in order to minimize total cost.
- b. How many hours should each graphic designer be assigned to the project? What is the total cost?
- c. Suppose Lisa could be assigned more than 50 hours. What would this have on the optimal solution? Explain.
- d. If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change?
Explain. 1. 5 National Insurance Associated carries an investment portfolio of stocks, bonds, and other investment alternatives. Currently, $200,000 of funds are available and must be considered for new investment opportunities. The four stock options National is considering and the relevant in Table 1. 2 Table 1: Problem 1.
|Price per share||$100||$50||$80||$40|
|The annual rate of return||0. 12||0. 08||0. 06||0. 10|
|Risk measure per dollar invested||0. 10||0. 07||0. 05||0. 8|
National’s top management has stipulated the following investment guidelines: The annual rate of return for the portfolio must be at least 9% and no one stock can account for more than 50% of the total dollar investment.
- a. Use linear programming to develop an investment portfolio that minimizes risk.
- b. If ignores risk and uses a maximum return-on-investment strategy, what is the investment portfolio?
1. 6 Greenville Cabinet received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf speakers and 4,100 ? or speakers over the next two months, with the delivery schedule as given in Table 2. Table 2:
Problem 1. 6
|Model||Month 1||Month 2|
Greenville estimates that the production time for each bookshelf model is 0. 7 hours and the production time for the model is 1 hour. The raw material costs are $10 for each bookshelf model and $12 for the model. Labor costs are $22 per hour. Greenville has up to 3,400 hours of production time available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. Formulate the problem to determine the numbers of units 3 that should be manufactured each month to minimize total production and storage costs.
1. 7 EZ-Windows, Inc. manufacturers replacement windows for the home remodeling business. In January, the company produces 15,000 windows and ended the month with 9,000 windows in inventory. EZ-Windows’ management team would like to develop a production schedule for the next three months. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a similar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown in Table 3, the management team does not think a smooth production schedule with the same production quantity each month possible.
Table 3: Problem 1. 7
The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1. 00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0. 65 for each unit decrease in the production level. Ignoring production and inventory carrying costs, formulate a linear programming model that will minimize the cost of changing production levels while still satisfying the monthly sales forecasts.
1. 8 Two television stations compete with each other for viewing audience. Local programming options for the 5 PM weekday time slot include a sitcom rerun, an early news program, and a home improvement show. Each station has the same programming options and must make its pre-season program selection before knowing what the other television station will do. The viewing audience gains in thousands of viewers for station A are shown in Table 4. 4 Station A/Station B Sitcom Rerun News Program Home Improvement Table 4:
Problem 1. 8
Formulate a linear program to determine the optimal strategy for each station and then solve it. What is the value of the game?
1. 9 A local television station plans to drop three Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of four potential replacement programs. Estimates of the advertising revenue (in dollars) that can be expected for each of the new programs in the four vacated time slots are as in Table 5. Table 5:
Problem 1. 9
|5–6 PM||6–7 PM|
1. 10 Adirondack Paper Mills, Inc. operates paper plants in Augusta, Maine, and Tupper Lake, New York.
Warehouse facilities are located in Albany, New York, and Portsmouth, New Hampshire. Distributors are located in Boston, New York, and Philadelphia. The Augusta plant has a capacity of 300 units, and the Tupper Lake plant has a capacity of 100 units. Boston has a demand of 150 units, New York has a demand of 100 units, and Philadelphia has a demand of 150 units. The unit transportation costs (in dollars) for shipments from the two plants to the two warehouses are presented in Table 6 and those from the two warehouses to the three 5 distributors.
Problem 1. 10 a. Draw the network representation of the Adirondack Paper Mills problem.
- a. Formulate the Adirondack Paper Mills problem as a linear programming problem.
- b. Solve the linear program to determine the minimum cost shipping schedule for the problem.
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