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 8 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. 1200 lb of cast iron and 1500 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