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MGMT 4600 Chapter 2 Homework Assignment - Linear Programming Exercises

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Question;Linear Programming Exercises2) The employee credit union at State University is planning the usage of funds for the coming year. The credit union makes four types of loans to its members. In addition, it invests in "risk-free" securities in order to stabilize income. The various revenue producing investments together with annual rates of return are as follows:Loan/Investment Type Annual Rate of ReturnSecured loans:Automobile0.08 (8%)Furniture0.10Other0.11Signature loans0.12Risk free securities0.09State laws and credit union policies impose the following restrictions on the composition of the credit union's loans and investments:1. "Risk-free" securities may not exceed 30% of the total funds.2. "Signature loans" must be at least 5% but no more than 10% of the total funds.3. "Furniture loans" plus "other secured loans" may not exceed 50% of the three types of secured loans.4. "Signature loans" plus "other secured loans" may not exceed the amount invested in "risk-free" securities.If the firm has $2 million available for loans and investments, how should the funds be allocated?Formulate as an LP.51. English Motors, Ltd. (EML), developed a new all-wheel-drive sports utility vehicle. As part of the marketing campaign, EML produced 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 sports utility vehicles offered by competitors, EML refers to these two target markets as the current customer market and the new customer market. Individuals who receive the new promotion video will also receive a coupon for a test drive of the new EML model for one weekend. A key factor in the success of the new promotion is the response rate, the percentage of individuals who receive the new promotion and test drive the new model. EML estimates that the response rate for the current customer market is 25% and the re- sponse rate for the new customer market is 20%. For the customers who test drive the new model, the sales rate is the percentage of individuals that make a purchase. Marketing re- search studies indicate that the sales rate is 12% for the current customer market and 20% for the new customer market. The cost for eachpromotion, excluding the test drive costs, is $4 for each promotion sent to the current customer market and $6 for each promotion sent to the new customer market. Management also speci?ed that a minimum of 30,000 current customers should test drive the new model and a minimum of 10,000 new cus- tomers should test drive the new model. In addition, the number of current customers who test drive the new vehicle must be at least twice the number of new customers who test drive the new vehicle.If the marketing budget, excluding test drive costs, is $1.2 million, how many promotions should be sent to each group of customers in order to maximize total sales?

 

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