MGM 3164 -- Sample LP Problems - Exercises
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MGM 3164 -- Sample LP Problems - Exercises
Production Application
1) Par Inc is a small manufacturer of golf equipment and supplies whose management has decided to move into the market for medium and high priced golf bags. Par’s distributor is very enthusiastic and has agreed to buy all the golf bags for the next 3 months. After a thorough investigation of the steps involved in
manufacturing a golf bag and the corresponding operation times are:
Operation |
Prodn time for Standard bag in hrs |
Prodn time for Deluxe bag in hrs |
Cutting and Dyeing |
7/10 |
1 |
Sewing |
½ |
5/6 |
Finishing |
1 |
2/3 |
Inspection and Packaging |
1/10 |
1/4 |
Par’s production is constrained by a limited number of hours available in each department. After studying the work load projections, the director of manufacturing estimates that 630 hours of cutting and dyeing, 600 hours of sewing, 708 hours of finishing, and 135 hours for inspection and packaging are available for the production of golf bags for the next 3 months. The accounting department has worked out the profit contribution from each product. The profit contributions are $10 for every standard bag and $ 9 for every deluxe bag produced. Formulate a LP model
Marketing Application
2) EML has developed a new all-wheel-drive sports utility vehicle. As part of the marketing campaign, EML has developed a video-tape sales presentation to send to both owners of current EML four-wheel- drive vehicles as well as to owners of four-wheel-drive vehicles offered by competitors. EML refers to these target groups as current customer and new customer. Individuals who receive the new promotion video will also receive a coupon for the test drive of new EML model. A key factor in the success is the response rate, the %age of individuals that receives the new promotion and test drive the vehicle. EML estimates that the response rate for the current customer market is 25% and response rate for the new market is 20%. For the customers who test drive the new model the sales rate is the %age of individuals that makes a purchase. Marketing studies indicate that the sales rate is 12% for the current customer market and 20% for the new customer market. The cost for each promotion, excluding the test drive costs are $4 for each promotion sent to the current customer market and $6 for each promotion sent to the new customer market. Management has also specified that a minimum of 30,000 current customers should test drive the new model and a minimum of 10,000 new customers should test drive the new model. In addition, the number of current customers that test drive the vehicle must be at least twice the number of new customers. If the marketing budget, excluding test drive costs, is $1,200,00, how many promotions should be sent to each group of customers in order to maximize total sales?
Finance Application
3) Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: stock fund and money market fund. Each unit of stock fund costs $50 and provides an annual return of 10%; each unit of money market fund costs $100 and provides the annual rate of return of 4%.
The client wants to minimize the risk subject to the annual income from the investment be at least $60,000. According to Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8 and each unit invested in money market fund has a risk index of 3; the higher risk associated with the stock fund simply indicates that it is the riskier investment. Innis’s client has also specified that at least $300,000 be invested in the money market fund. Formulate an LP model.
4) The New England Cheese Company produces two types of cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spread are packaged in 12-ounce containers (16 ounces = 1 pound) and then sold. The Regular blend contains 80% mild cheddar and 20% extra sharp cheese . The Zesty blend contains 60% mild cheddar and 40% extra sharp cheese. This year the local dairy has offered to provide 8100 pounds of mild cheddar cheese at $1.20 per pound and up to 3000 pounds of extra sharp cheese at $1.40 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce? Formulate an LP model.
2022-09-16