3. Problem (30 points total) Consider the following problem. Maximize Z = 8x1 + 4x: + 6X3 + 3x4 + 9X5, subject to x1 + 2x2 + 31::3 + 3X4 5 180 (resource 1) 4x1 + 3x2 + 2x3 + x4 + XS S 270 (resource 2) x1+ 3x2+ X4 + 331,; S 180 (resource 3) and xj 2 0, j:1,...5. You are given the fact that the basic variables in the optimal solutions are x3, x1)and xsand that 310'1 11 _3 1 241 =i_6 9_3 27 013 2 _310 a) (10 pts) Use the given information to identify 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.