Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses $50$ units of synthetic fiber, requires $25$ hours of production time, and needs $20$ units of foam backing. Each roll of Grade Y carpet uses $40$ units of synthetic fiber, requires $28$ hours of production time, and needs $15$ units of foam backing.