Question: 1 (5 points). Consider the linear programming problem Maximize z = 1:1 + 332 subject to sc1+:r2 g 1 33:1 + m2 5 13 :32

1 (5 points). Consider the linear programming problem Maximize z = 1:1 + 332 subject to sc1+:r2 g 1 33:1 + m2 5 13 :32 Z 1 1121 2 0, $2 2 0. (a) Sketch the feasible region. (b) Sketch a few level curve of the objective function. (c) Find the optimal solution by the graphical method. 2 (5 points). Consider the linear programming problem Maximize z = 21:1 231:2 + 311:3 subject to ~31 + 3:2 + 323 g 4 23:1 5'52 + 553 $ 2 331 +332 +3553 13 33120, 93220: 113320- Work through the simplex method step by step to solve the problem. Include details on optimality test, ratio test, entering variable, and leaving variable from one feasible echelon form to the next. State at each step the basic feasible solution. Intermediate tableaus between feasible echelon forms are not necessary to include, which can be substituted in place of brief descriptions on elementary row operations, such as 2R1+R0 ) R0, 2R2, etc

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