30. Solve the following LP problem and answer the questions regarding a firm that manufactures both lawn mowers (x1) and snowblowers (x2).

(i) What is the best product mix? What is the optimal profit?
(ii) What are the shadow prices of the resources? When the optimal solution has been reached, which resource has the highest marginal value?
(iii) Over what range in each of the RHS values are these shadows valid?
(iv) What are the ranges over which the objective function coefficients can vary for each of the two decision variables?
(v) State the dual to this problem and write its solution.

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Maximise Subject to Z=30x + 80x2 2x+4x2 1,000 labour hours available 6x1 + 2x2 1,200 lb. of steel available x2 200 snowblower engines available