Gulf Coast Electronics is ready to award contracts for printing its annual repor

Question

Gulf Coast Electronics is ready to award contracts for printing its annual report. For the past several years, Johnson Printing and Lakeside Litho printed the four-color annual report. A new firm, Benson Printing, has inquired about the possibility of doing a portion of the printing. The quality and service level provided by Lakeside Litho has been extremely high; in fact, only 0.5% of their reports have been discarded because of quality problems. Johnson printing also has a historically high quality level, producing an average of only 1% unacceptable reports. Since Gulf Coast Electronics has had no experience with Benson Printing, they have estimated its defective rate to be 10%. Gulf Coast would like to determine how many reports should be printed by each firm to obtain 75,000 reports of acceptable quality. To ensure that Benson Printing will receive some of the contract, management has specified that the number of reports awarded to Benson Printing must be at least 10% of the volume given to Johnson Printing. In addition, the total volume assigned to Benson Printing, Johnson Printing, and Lakeside Litho should not exceed 30,000, 50,000, and 50,000 copies, respectively. Because of the long-term relationship that has developed with Lakeside Litho, management also has specified that at least 30,000 reports should be awarded to Lakeside Litho. The cost per copy is $2.45 for Benson Printing, $2.50 for Johnson Printing, and $2.75 for Lakeside Litho. Formulat and solve a 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.

I am confused to what the constraints are for this problem. Thank you for your help

Explanation / Answer

Let x1=number of reports awarded to Benson Printing

x2=number of reports awarded to Johnson Printing

x3=number of reports awarded to Lakeside Litho

a. Minimize: 2.45x1+2.50x2+2.75x3

Subject to

x1+x2+x3<=75000

x1-0.10x2<=0

x3>=30000

x1<=30000

x2<=50000

x3<=50000

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