please show work, and type so i can better understand.

3. Consider the following linear program: Max 3x1 +4x2 (s Profit) s.t. x1 + 3x2-12 2x1 + x2 = 8 x =3 xl. x2 > 0 The Management Scientist provided the following solution output: OPTIMAL SOLUTION Objective Function Value = 20.000 Variable Value Reduced Cost x 2.4000.000 X2 3.2000.000 Constraint Slack/Surplus Dual Price 0.000 1.000 10.000 1.000 10.600 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 1.333 3.000 18.000 X2 1.500 4.000 19.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 19.000 12.000 24.000 4.000 8.000 19.000 2.400 3.000 No Upper Limit a. What is the optimal solution including the optimal value of the objective function? b. Suppose the profit on xl is increased to S8. Is the above solution still Joptimal? What is the value of the objective function when this unit profit Jis increased to $8? c.JIf the unit profit on x2 was S9 instead of S4, would the optimal solution change? If yes, what is the optimal solution? d. If simultaneously the profit on xl was reduced to $2.0 and the profit on x2 was raised to $5.5, what is the optimal solution