3. Consider the following linear program: MIN 6x1 + 9x2 (s cost) s.t. X1 + 2x2 58 10x1 + 7.5x2 30 x2 22 x1,x220 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value - 27.000 Variable X1 Value 1.500 2.000 Reduced Cost 0.000 0.000 Constraint Slack/Surplus 2.500 0.000 0.000 Dual Price 0.000 -0.600 -4.500 OBJECTIVE COEFFICIENT RANGES Variable X1 Lower Limit 0.000 4.500 Current Value 6.000 9.000 Upper Limit 12.000 No Upper Limit RIGHT HAND SIDE RANGES 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 a. b. c. d. What is the optimal solution including the optimal value of the objective function? Suppose the unit cost of Xi 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 xa be decreased without concern for the optimal solution changing? If simultaneously the cost of x, was raised to $7.5 and the cost of x2 was reduced to S6, 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