Question

Solve the following linear system using solver. Provide both the optimal solution and the optimal value of the objective function at the optimal solution.

max TO0x,x 2x +2x, S 16 B 20

Using the results you get in Excel, calculate the following (by hand): Please show all work in excel.

1. Slack/surplus for every constraint.
2. Range of optimality for each decision variable.
3. Allowable increase (AI) and allowable decrease (AD) for each decision variable.

Answer 1

Given form the data is * let us consider the equation are the optional solution and the optimal value and its objective function at the optimal solution * let us the equations are Max = 10 x_1 + x_2 implies z = 10 x_1 + x_2 {where x_1 = x x_2 = y} s,t 3 x + 2 y lessthanorequalto 12 rightarrow A 2 x + 2 y lessthanorequalto 16 rightarrow B x - y lessthanorequalto 2 rightarrow C x, y graterthanorequalto 0 * from the plotted on the graph we get rightarrow from A implies 3 x + 2 y = 12 rightarrow from B 2 x + 2 y = 16 rightarrow form C x - y = 2 rightarrow these are the points is (0, 0) (2, 0) (0, 8) (5, 1) is the points of interest and made area implies these Max values are z = 10 x + y