Work through the simplex method step by step to solve the problem.

1. Consider the following problem. Maximize Z _ 5×1 _ 4×2 _ x3 _ 3×4, subject to
3×1 _ 2×2 _ 3×3 _ x4 _ 24 (resource 1)

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3×1 _ 3×2 _ x3 _ 3×4 _ 36 (resource 2)
and
x1 _ 0, x2 _ 0, x3 _ 0, x4 _ 0.
(a) Work through the simplex method step by step to solve the problem.
 
(b) Identify the shadow prices for the two resources and describe their significance.
 
(c) Use a software package based on the simplex method to solve the problem and then to generate sensitivity information. Use this information to identify the shadow price for each resource, the allowable range to stay optimal for each objective function coefficient, and the allowable range to stay feasible for each right-hand side.