3. Consider the following linear program: MIN 6x1 + 9x2 (s cost) x1 +212 58 10x + 7.5x2 2 30 X2 X1, X220 s.t. The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 27.000 Variable X1 X2 Value 1.500 2.000 Reduced Cost 0.000 0.000 Constraint 1 2 3 Slack/Surplus 2.500 0.000 0.000 Dual Price 0.000 -0.600 4.500 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit X1 0.000 X2 4.500 RIGHT HAND SIDE RANGES Current Value 6.000 9.000 Upper Limit 12.000 No Upper Limit Constraint Lower Limit 5.500 15.000 0.000 Current Value 8.000 30.000 2.000 Upper Limit No Upper Limit 55.000 4.000 2 3 c. a. What is the optimal solution including the optimal value of the objective function? b. Suppose the unit cost of x is decreased to $4. Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4? How much can the unit cost of x2 be decreased without concern for the optimal solution changing? d. If simultaneously the cost of xi was raised to $7.5 and the cost of x2 was reduced to $6, would the current solution still remain optimal? If the right-hand side of constraint 3 is increased by 1, what will be the effect on the optimal solution? e