Please write out the minimization problem and decision variables. There is a constraint for no more than two states that can be selected.

BestChip: Expansion Strategy BestChip (BC) is a large nationwide corporation that produces low-fat snack products for an expanding market (pun intended). Basically, BC takes materials (corn, wheat, and potatoes) and turns them into two types of snacks: chips (regular and green onion) and party mix (one variety). BC is expanding into the western United States and is considering sites for lo- cating production facilities. BC currently has eight candidate sites. Table 20 shows the sites' purchase prices and the purchase and shipping cost per ton of each material to each site. The purchase cost represents the yearly amortized cost of opening and operating the site (exclusive of TABLE 20 Site Information and Material Shipping Cost Material Shipping Cost ($/Ton) Corn Wheat Potato Site Location 10 12 9 Yuma, AZ Fresno, CA Tucson, AZ Pomona, CA Santa Fe, NM Flagstaff, AZ Las Vegas, NV St. George, UT Purchase Cost ($/Year) 125,000 130,000 140,000 160,000 150,000 170,000 155,000 115,000 11 8 5 8 10 7 14 12 12 15 16 11 15 14 10 11 9 10 13 14 8 TABLE 21 Demand Information Demand Green Onion Company Location Regular Party Mix Jones YZCO Square Q AJ Stores Sun Quest Harm's Path Salt Lake City Albuquerque Phoenix San Diego Los Angeles Tucson 1,300 1,400 1,200 1,900 1,900 1,500 900 1,100 800 1,200 1,400 1,700 1,700 1,800 2,200 2,300 1,400 1,000 TABLE 22 Product-Ingredient Mix Ingredient Wheat Product Corn Potato Regular chips Green onion chips Party mix 70 30 20 15 10 55 30 20 50 shipping costs). Each site may produce as many as 20,000 tons of product per year. BC has six major customers, and all demand is shipped by truck from the plant to the customer ware- house. The shipping cost depends on the tonnage and distance and comes to $0.15 per ton-mile. The cus- tomers, their location, and their yearly demand in tons for each product are listed in Table 21. You must meet demand. The makeup of the products does not depend on the production plant. Table 22 gives the product- ingredient mix data. The company requires that we consolidate our business, so we cannot locate plants in more than two states. For this analysis, ignore the differences in property and income tax rates between the states (this is usually critical, but it gets us far afield of the key issue of math programming). In addition, many critical factors actu- ally determine locations, for example, the method of financing the site purchase will also be a major factor in the decision-but we will ignore that also. Your job is to determine how we should expand into the west and develop alternatives. Questions you should answer include: What sites should be selected? How should the customers be served? If gasoline gets more expensive and our trucking costs change, then how is the recommendation affected? If rail freight costs for material shipping increase, then how is the recommendation affected? Please consider other sensitivity-analysis issues that you feel might be important for management's decision-making process. BestChip: Expansion Strategy BestChip (BC) is a large nationwide corporation that produces low-fat snack products for an expanding market (pun intended). Basically, BC takes materials (corn, wheat, and potatoes) and turns them into two types of snacks: chips (regular and green onion) and party mix (one variety). BC is expanding into the western United States and is considering sites for lo- cating production facilities. BC currently has eight candidate sites. Table 20 shows the sites' purchase prices and the purchase and shipping cost per ton of each material to each site. The purchase cost represents the yearly amortized cost of opening and operating the site (exclusive of TABLE 20 Site Information and Material Shipping Cost Material Shipping Cost ($/Ton) Corn Wheat Potato Site Location 10 12 9 Yuma, AZ Fresno, CA Tucson, AZ Pomona, CA Santa Fe, NM Flagstaff, AZ Las Vegas, NV St. George, UT Purchase Cost ($/Year) 125,000 130,000 140,000 160,000 150,000 170,000 155,000 115,000 11 8 5 8 10 7 14 12 12 15 16 11 15 14 10 11 9 10 13 14 8 TABLE 21 Demand Information Demand Green Onion Company Location Regular Party Mix Jones YZCO Square Q AJ Stores Sun Quest Harm's Path Salt Lake City Albuquerque Phoenix San Diego Los Angeles Tucson 1,300 1,400 1,200 1,900 1,900 1,500 900 1,100 800 1,200 1,400 1,700 1,700 1,800 2,200 2,300 1,400 1,000 TABLE 22 Product-Ingredient Mix Ingredient Wheat Product Corn Potato Regular chips Green onion chips Party mix 70 30 20 15 10 55 30 20 50 shipping costs). Each site may produce as many as 20,000 tons of product per year. BC has six major customers, and all demand is shipped by truck from the plant to the customer ware- house. The shipping cost depends on the tonnage and distance and comes to $0.15 per ton-mile. The cus- tomers, their location, and their yearly demand in tons for each product are listed in Table 21. You must meet demand. The makeup of the products does not depend on the production plant. Table 22 gives the product- ingredient mix data. The company requires that we consolidate our business, so we cannot locate plants in more than two states. For this analysis, ignore the differences in property and income tax rates between the states (this is usually critical, but it gets us far afield of the key issue of math programming). In addition, many critical factors actu- ally determine locations, for example, the method of financing the site purchase will also be a major factor in the decision-but we will ignore that also. Your job is to determine how we should expand into the west and develop alternatives. Questions you should answer include: What sites should be selected? How should the customers be served? If gasoline gets more expensive and our trucking costs change, then how is the recommendation affected? If rail freight costs for material shipping increase, then how is the recommendation affected? Please consider other sensitivity-analysis issues that you feel might be important for management's decision-making process