Problem 2. (24 points) The Food Max grocery store sells three brands of milk in half-gallon cartons - its own brand, a local dairy brand and a national brand. The profit from its own brand is $0.97 per carton, the profit from the local dairy brand is $0.83 per carton and the profit from the national brand is $0.69 per carton. The total refrigerated shelf space allotted to half-gallon cartons of milk is 36 square feet per week. A half-gallon carton takes up 16 square inches of shelf space. The manager knows that each week, Food Max always sells more of the national brand than the local dairy brand and its own brand combined and at least three times as much as the national brand as its own brand. In addition, the dairy can supply only 10 dozen cartons per week in order to maximize profit. f. Formulate an LP model for this problem. g. Solve this model using the spreadsheet. h. If Food Max could increase its shelf space for half-gallon cartons of milk, how much would profit increase per carton? Explain precisely. i. If Food Max could get the local dairy to increase the amount of milk it could supply each week, would it increase profit? Explain precisely. j. Food Max is considering discounting its own brand in order to increase sales. If it were to do so, it would decrease the profit margin for its own brand to $0.86 per carton, but it would cut the demand for the national brand relative to its own brand in half. Discuss whether the store should implement the price discount