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 grate requires 3 lb of cast iron and 6 min of labor. to produce each model b grate requires 4 lb of cast iron and 3 min of labor. the profit for each model a grate is $3.50, and the profit for each model b grate is $3.00. also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. because of a backlog of orders for model a grates, kane's manager had 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