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Formulate but do not solve the following exercise as a linear programming problem. Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type A vessel, x, has 45 deluxe cabins and 165 standard cabins, whereas a type B vessel, y, has 80 deluxe cabins and 125 standard cabins. Under a charter agreement with Odyssey Travel Agency' Deluxe River Cruises is to provide Odyssey with a minimum of 380 deluxe and 660 standard cabins for their 15-day cruise in May. It costs $45,000 to openate a type A vessel and $56,000 to operate a type B vessel for that period. HowI many of each type of vessel should be used in order to keep the operating costs, C (in dollars), to a minimum? Minimize C - 15;: + 20y subject to the constraints deluxe cabins standard cabins Formulate but do not solve the following exercise as a linear programming problem. Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 5 lb of cast iron and 5 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. 1300 lb of cast iron and 1200 min of labor are available for the production of grates per day. Because of a backlog of orders on model A grates, the manager of Kane Manufacturing has decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit P in dollars? Maximize P = subject to the constraints cast iron labor model A y 20