3. Problem (30 points total) Consider the following problem. Maximize Z = 8x1 + 4x2 + 6X3 + 3x4 + 9X5, subject to x1 + 2x2 + 3X3 + 3x4 5 180 (resource 1) 4x1 + 3x2 + 2x3 + x4 + x5 5 270 (resource 2) x1+ 3x2+ x4+ 3x5 3 180 (resource 3) and xj 30, j=1,...5. You are given the fact that the basic variables in the optimal solutions are x3: xlrand x5and that 310'1 1131 241 =1-6 93 27 013 2310 a} {10 pts) Use the given information to identil'vr the optimal solution. b} {10 pts) Use the given information to identify the shadow prices for the three resources. c) {10 pts) Use the results from part b to tell what happens to the optimal value if the right hand side of constraint equation 1 {resource 1) changed from 180 to 181; What happens to the optimal value if the right hand side of constraint equation 2 (resource 2} changed from 270 to 268