1. Consider the following problem. Maximize Z = x1 7x2 + 3x3 subject to 2x1 + x2 x3 4 4x1 3x2 2 3x1 +2x2 +x3 3 x1,x2,x3 0 (a) Work through the simplex method step by step to solve the problem. (b) Identify the shadow prices for the three 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 for each objective function coefficient, and the allowable range for each righthand side.