A stereo mail order center has $9,000$ cubic feet available for storage of its private label loudspeakers. The Z$3$ speakers

cost $$255$ each and require $6$ cubic feet of space; the $Zx$ speakers cost $$120$ each and require $3$ cubic feet of space; and

the $Z4$ model costs $$60$ and requires $1$ cubic foot of space. The demand for the $Z3$ is at most $30$ units per month. The

wholesaler has $$100,000$ to spend on loudspeakers this month. Each $Z3$ contributes $$125,$ each $Zx$ contributes $$55,$

and each Z$4$ contributes $$25$ to profit. The objective is to maximize total profit. Formulate this problem as a linear

program.