You’re working as an Industrial Engineer at Dell. Customers purchase laptops throughout the year, but before each semester, university bookstores order large quantities to have in stock for students and staff. The business intelligence unit just released the initial demand forecasts for January orders in the Midwest region, and your manager, Alejandro, stopped by your office to discuss the production plans. He’d like to know the most profitable way to fill all of the orders and asked you to send him a report by next Thursday. He wants a breakdown of how many units of each type of laptop the manufacturing division should plan to produce. Because it’s a draft plan, Alejandro is fine with non-integer estimates. They have the option to produce one of four types in the XPS product line. There are two sizes – 13in and 15in, and both have a touchscreen and non-touchscreen option. The prices of the non-touchscreen laptops are $800 and $900 for 13in and 15in, respectively, and the price of the touchscreen option on either size is an additional $200. The production costs of the 13in laptop are $600 (non-touchscreen) and $650 (touch), and the 15in laptop costs $625 (non-touch) and $675 (touch). The forecast predicts a total of 10,000 units to be ordered. It says 4,000 will be for 13in laptops, 2,000 will be for 15in laptops, and the remaining 4,000 units won’t have a size specified. They predict exactly 3,000 touchscreens will be ordered but can’t say what size. Space may also be a limiting factor - Dell has set aside 3,800 cubic feet of storage space for these orders. The boxes for the 13in laptops take up 0.3 cubic feet, and the boxes for the 15in laptops take up 0.45 cubic feet.