Use the simplex algorithm to solve the following LP max z = 3x_1 + 4x_2 s.t x_1

Question

Use the simplex algorithm to solve the following LP max z = 3x_1 + 4x_2 s.t x_1 + 2x_2 lessthanorequalto 8 3x_1 + x_2 lessthanorequalto 14 x_1,x_2 Greaterthanorequalto 0 (a) Write into a standard form by introducing slack variables. (b) Write the initial tableau and solve by simplex method. Be sure to write basic variables at each step. (c) Optimal solution at x_1 =, x_2 =, s_1 = s_2 =, optimal value= (d) Identify whether the above LP has alternative solutions, unique solution, or unbounded region

Explanation / Answer

Standard linear programming problem can be solved by graphical method as there are only two variables. Solution using simplex method is as follows: The optimum solution is unique and bounded.

x1 x2 RHS Dual Maximize 3 4 constraint1 1 2 <= 8 1.8 constraint2 3 1 <= 14 0.4 Solution-> 4 2 20

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