A stereo mail order center has $8,000$ cubic feet available for storage of its private label loudspeakers. The ZAR$3$ speakers cost $$295$ each and require $4$ cubic feet of space; the ZAR$2$ax speakers cost $$110$ each and require $3$ cubic feet of space; and the ZAR$4$ model costs $$58$ and requires $1$ cubic foot of space. The demand for the ZAR$3$ is at most $20$ units per month. The wholesaler has $$100,000$ to spend on loudspeakers this month. Each ZAR$3$ contributes $$105,$ each ZAR$2$ax contributes $$50,$ and each ZAR$4$ contributes $$28.$ The objective is to maximize total contribution. Formulate this problem as a linear program.