Industrial Packaging Solutions (IPS) is a manufacturer of corrugated fiberboard shipping boxes used by companies across the United States. It sells to wholesalers, who in turn sell to resellers or end-user customers. Final products are consolidated on standard shipping pallets of uniform dimensions and weight. Because of this, the cost to ship a pallet to a single destination is the same regardless of the type of box loaded on the pallet. The standard unit for sales and operations planning at IPS is a pallet load. After recently opening a new factory to satisfy growing demand for its products, IPS is concerned about allocating demand from its customers to the facilities in its production network. It wants to do so in a way that minimizes the total cost of shipping final products to the wholesalers. It currently has three factories that service a network of seven major wholesalers. Relevant data for the next year are shown in the table below. Factory Location Production Capacity (pallets1,000) Denver, CO 25 Chicago, IL 50 Baltimore, MD 35 Wholesaler Location Spokane, WA Demand (pallets1,000) 8.5 Los Angeles, CA 19.6 Kansas City, MO 9.3 Minneapolis, MN 8.8 Indianapolis, IN 11.8 Atlanta, GA 13.6 New York City, NY 17.2 Based on contracts with its transportation suppliers, IPS is confident that the following transportation rates will be valid over the next year. Rates provided are to transport one pallet of product. There is no quantity discount given for volume shipments. Destination City and Transportation Rates Factory Location Spokane L.A. K.C. Minn. Indy. Atlanta NYC Denver, CO $42 $49 $45 $54 $56 $465 $70 Chicago, IL $65 $69 $49 $38 $32 $45 $50 Baltimore, MD $75 $77 $68 $62 $43 $44 $35 Develop a low-cost transportation plan for IPS for the upcoming year using linear programming method. The plan should consider all related factors that can be managed, and variables should be defined to represent these factors. Please answer the questions below. 1. Identify all the relevant factors that can be managed and define variables to represent them. (15 points) 2. Define the total cost using the variables defined in step 1. (15 points) 3. Formulate all necessary constraints that will help you compute the minimum total cost. (10 points) By completing these steps, you will be able to develop an optimized low-cost transportation plan for IPS that will help to reduce their transportation expenses for the upcoming year. Note that there is no need to do any computation.