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 SO.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 store manager knows that each week Food Max always sells more of the national brand than of the local dairy brand and its own brand combined and at least three times as much of the national brand as its own brand. In addition, the local dairy can supply only 10 dozen cartons per week. The store manager wants to know how many half-gallon cartons of each brand to stock each week in order to maximize profit.

a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.

Sean lives in dallas and runs a business that sells boats. in an average year, he receives $722,000 from selling boats. of this sales revenue, he must pay the manufacturer a wholesale cost of $422,000; he also pays wages and utility bills totaling $268,000. he owns his showroom; if he chooses to rent it out, he will receive $2,000 in rent per year. assume that the value of this showroom does not depreciate over the year. also, if sean does not operate this boat business, he can work as a paralegal, receive an annual salary of $21,000 with no additional monetary costs, and rent out his showroom at the $2,000 per year rate. no other costs are incurred in running this boat business. identify each of sean's costs in the following table as either an implicit cost or an explicit cost of selling boats. implicit costexplicit costthe wages and utility bills that sean pays the rental income sean could receive if he chose to rent out his showroom the salary sean could earn if he worked as a paralegal the wholesale cost for the boats that sean pays the