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 $4.00, and the profit for each model B grate is $4.00. 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

Lipman auto parts, a family-owned auto parts store, began january with $10,300.00 in cash. management forecasts that collections from credit customers will be $11,400.00 in january and $14,800.00 in february. the store is scheduled to receive $5,000.00 in cash on a business note receivable in january. projected cash payments include inventory purchases ($13,000.00 in january and $13,600.00 in february) and operating expenses ($2,700.00 each month). lipman auto parts' bank requires a $10,000.00 minimum balance in the store's checking account. at the end of any month when the account balance dips below $10,000.00, the bank automatically extends credit to the store in multiples of $1,000.00. lipman auto parts borrows as little as possible and pays back loans in quarterly installments of $2,000.00, plus 4 percent interest on the entire unpaid principal. the first payment occurs three months after the loan.