A firm that makes three products and has three machines available as resources constructs the following LP problem:

Solve this problem by computer and answer these questions:
(a) Before the third iteration of the simplex method, which machine still has unused time available?
(b) When the final solution is reached, is there any unused time available on any of the three machines?
(c) What would it be worth to the firm to make an additional hour of time available on the third machine?
(d) How much would the firm’s profit increase if an extra 10 hours of time were made available on the second machine at not extracost?

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Maximize profit-4X1 + 4x, + 7X3 subject to IXi 7X + 4X3 100 (hours on machine 1) 2x, + 1Xy + 7X3-1 10 (hours on machine 2) 8X 4X2 t 1X3110 (hours on machine 3)