Xara Stores in the United States stocks a particular type of designer denim jeans that is manufactured in China and Brazil and imported to the Xara distribution center in the United States. It orders 500 pairs of jeans each month from its two suppliers. The Chinese supplier charges Xara $11 per pair of jeans, and the Brazilian supplier charges $16 per pair (and then Xara marks them up almost 1,000%). Although the jeans from China are less expensive, they also have more defects than those from Brazil. Based on past data, Xara estimates that 7% of the Chinese jeans will be defective compared to only 2% from Brazil, and Xara does not want to import any more than 5% defective items. However, Xara does not want to rely only on a single supplier, so it wants to order at least 20% from each supplier every month.
(a) Formulate a linear programming model for this problem.
(b) Solve the linear programming model for Xara Stores graphically and by using the computer.
(c) If the Chinese supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, what would be the effect on the solution?
(d) If Xara Stores decided to minimize its defective items while budgeting $7,000 for purchasing the jeans, what would be the effect on the solution?