Strictly solve c),d), and e) only!!

1. Exercise (2.5 pts) Assume the following linear program: Maximizez=x1+2x2+4x3 subject to: 3x1+2x2+5x3x1+4x2+x32x1+2x3x1x2x3361812000 (a) Carry out the first step of the simplex method in algebraic form so as to move from the initial basic feasible solution to the next basic feasible solution. (b) Write the dual of this problem. (c) Solve the original problem (not the dual) with, e.g., Excel Solver. (d) Use the information of the sensitivity report to obtain the solution of the dual (when solving with Excel Solver, tick "Sensitivity" among the list of Reports next to "Keep Solver Solution" after solving). (e) What else do you learn from the report