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# Quantitative Methods of Business/ ANDERSON, SWEENEY, WILLIAMS Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution Gulf...

Gulf Coast Electronics (GCE) is ready to award contracts for printing their annual report. For the past several years, the four-color annual report has been printed by JP and LL. A new firm, inquired into the possibility of doing a portion of printing. The quality and service level of LL has been extremely high; in fact, only 0.5% of their reports had to be discarded because of quality problems. JP has also had a high quality level historically, producing an average of only 1% unacceptable reports. Because GCE has had no experience with BP, they estimated their defective rate to be 10%. GCE would like to determine how many reports should be printed by each firm to obtain 75,000 acceptable-quality reports. To ensure that BP will receive some of the contract, management specified that the number of reports awarded to BP must be at least 10% of the volume given to JP. In addition, the total volume assigned to BP, JP and LL should not exceed 30,000, 50,000 and 50,000 copies, respectively. Because of the long-term relationship with LL, management also specified that at least 30,000 reports should be awarded to LL. The cost per copy is \$ 2.45 for BP, \$ 2.50 for JP, and \$ @.75bfor LL.
a) Formulate and solve linear program for determining how many copies should be assigned to each printing firm to minimize the total cost of obtaining 75,000 acceptable-quality reports?
b) Suppose that the quality level for BP is much better than estimated. What effect, if any, would this quality level have?
c) Suppose that management is willing to reconsider their requirement that LL be awarded at least 30,000 reports. What effect, if any, would this consideration have?
Quantitative Methods of Business/ ANDERSON, SWEENEY, WILLIAMS Chapter 8 Linear Programming: Sensitivity Analysis and Interpretation of Solution Gulf Coast Electronics (GCE) is ready to award contracts for printing their annual report. For the past several years, the four-color annual report has been printed by JP and LL. A new firm, inquired into the possibility of doing a portion of printing. The quality and service level of LL has been extremely high; in fact, only 0.5% of their reports had to be discarded because of quality problems. JP has also had a high quality level historically, producing an average of only 1% unacceptable reports. Because GCE has had no experience with BP, they estimated their defective rate to be 10%. GCE would like to determine how many reports should be printed by each firm to obtain 75,000 acceptable-quality reports. To ensure that BP will receive some of the contract, management specified that the number of reports awarded to BP must be at least 10% of the volume given to JP. In addition, the total volume assigned to BP, JP and LL should not exceed 30,000, 50,000 and 50,000 copies, respectively. Because of the long-term relationship with LL, management also specified that at least 30,000 reports should be awarded to LL. The cost per copy is \$ 2.45 for BP, \$ 2.50 for JP, and \$ @.75bfor LL. a) Formulate and solve linear program for determining how many copies should be assigned to each printing firm to minimize the total cost of obtaining 75,000 acceptable-quality reports? b) Suppose that the quality level for BP is much better than estimated. What effect, if any, would this quality level have? c) Suppose that management is willing to reconsider their requirement that LL be awarded at least 30,000 reports. What effect, if any, would this consideration have?

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