Question 7 (15 points): MAX INTERNATIONAL is a company that manufactures 5 different types of printers. To manufacture each type of printers, different types of initial items are required to be assembled. The details of required items for different printers are given in Table 7. Table 7- The number of required items for different types of printers. Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Printer Type 1 1 7 3 4 2 Printer Type 2 7 0 6 7 5 2 Printer Type 3 6 0 5 0 4 1 Printer Type 4 0 3 4 0 6 4 Printer Type 5 2 1 6 4 3 This company has 7 different of customers around the country. The demands of these customers for different types of printers are given in Table 8. Table 8- The number of required items for different types of printers. Printer Type 1 Printer Type 2 Printer Type 3 Printer Type 4 Printer Type 5 Customer 1 477 446 406 446 108 Customer 2 417 395 616 333 632 Customer 3 687 610 660 595 23 Customer 4 668 327 314 344 334 Customer 5 652 481 599 357 574 Customer 6 384 540 584 345 433 Customer 391 683 326 357 496 The company buys the items of printers in batches from different suppliers. The details of batches provided by different suppliers are provided in Table 9. Table 9- The number of required items in each batch of suppliers. Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 A batch from supplier 1 1 7 6 9 1 2 A batch from supplier 2 7 0 6 7 5 2 A batch from supplier 3 6 0 5 0 A batch from supplier 4 3 4 0 6 4 NO A batch from supplier 5 1 6 4 3 7 To understand Table 9, note that the second row of this Table shows that a batch of items from supplier 1 includes 1 item of type 1, 7 items of type 2, 6 items of type 3, 9 items of type 4, 1 item of type 5, and 2 items of type 6. 7/8 Part a) Formulate a mathematical programming model to explain how the company must order batches from different suppliers to cover their demands. (7 points) Part b) Suppose that the company is allowed to not cover the whole demand of all customers. For example, the company may decide to provide only 400 printers of type 1 to customer 5, while this customer has requested for 652 units of this printer. For each unit of the demand that is not fulfilled, the company must pay a penalty that depend on the type of the printer. The details of penalties are given in Table 10. Table 10- Data of penalties. Printer Type 1 Printer Type 2 Printer Type 3 Printer Type 4 Printer Type 5 Penalty for not covering each unit of $500 $350 $400 $210 $150 demand How would you modify the mathematical model to address the additional information? (8 points)