42. Mega-Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the company has purchased is large enough to accommodate a store with 140,000 square feet of floor space. Based on marketing and demographic surveys of the area and historical data from its other stores, Mega-Mart estimates its annual profit per square foot for each of the store's departments to be as shown in the following table. Each department must have at least 15,000 square feet of floor space, and no department can have more than 20% of the total retail floor space. Men's, women's, and children's cloth- ing plus housewares keep all their stock on the retail floor; however, toys, electronics, and auto supplies keep some items (such as bicycles, televisions, and tires) in inventory. Thus, 10% of the total retail floor space devoted to these three departments must be set aside outside the retail area for stocking inventory. Mega-Mart wants to know the floor space that should be devoted to each department to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using the computer. Department Profit per ft.2 Men's clothing $4.25 Women's clothing 5.10 Children's clothing 4.50 Toys 5.20 Housewares 4.10 Electronics 4,90 Auto supplies 3.80 43. a. In Problem 42, Mega-Mart is considering purchasing a parcel of land adjacent to the current site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable Mega-Mart to increase the size of its store to 160,000 square feet. Discuss whether Mega-Mart should purchase the land and increase the planned size of the store. b. Suppose that the profit per square foot will decline in all departments by 20% if the store size increases to 160,000 square feet. (If the stock does not turn over as fast, increasing inventory costs will reduce profit.) How might this affect Mega-Mart's decision in (a)?V1 V2 Decision Variables O Objective Function Coefficient Constraints: LHS Sign RHS Constraint #1 Constraint #2 Constraint #3