Question

Given the following output, what would happen if the coefficient of X2 increased by 1 LINEAR PROGRAMMING PROBLEM MAX 31X1+35X2+32X3 S.T 1) 3X1+5X2+2X3>90 2) 6X1 7X2+8X3<150 3) 5x1+3X2+3X3120 OPTIMAL SOLUTION Objective Function Value 763.333 Variable Value Reduced 13.333 0,000 10.000 0.000 0.000 10.889 X1 X2 X3 Constraint Slack/Surplus Dual Price 0.000 0.000 23.333 0.778 5.556 0.000 OBJECTIVE COEFFICIENT RANGES Lower Current Upper Limit Value Limit No X1 30.000 31000 Upper Limit No X2 Lower 35.000 36.167 Limit No Limit X3 Lower 32.000 42.889 RIGHT HAND SIDE RANGES Lower Current Upper Limis Value Limit 77.647 90.000 107.143 126.000 150000 163.125 No 96.667 120.000 Upper Limit The value of the objective function would decrease by 10.

Answer 1

Answer: The value of objective function would increase by 10.

Explanation:

The current optimal solution holds if coefficient of X2 increases by 1. The current coefficient is 35 and new coefficient will be 36. From optimal solution we can see that the solution holds for coefficient upper limit of 36.167 for X2, therefore it will hold for coefficient value of 36.

Also,

As X2 = 10 so increase in coefficient by 1 will increase objective function value by 10.