Astereo mail order center has 8,000 cubic feet available for storage of its private label loudspeakers. the zar1 speakers cost $295 each and require 4 cubic feet of space; the zar2 speakers cost $110 each and require 3 cubic feet of space; and the zar3 model costs $58 and requires 1 cubic foot of space. the demand for the zar1 should be at least 20 units per month. the demand for zar2 should be at least 50 units per month. the wholesaler has $100,000 to spend on loudspeakers this month. each zar1 contributes $105, each zar2 contributes $50, and each zar3 contributes $28. the objective is to maximize total contribution. a) formulate this problem as a linear programming problem (define decision variables, objective function and constraints).
b) it has been determined that zar3 speakers are out of stock so cannot be ordered. solve the problem using solver.