Answer Questions 3 and 4 based on the following linear optimization problem. Maximize 10X1 + 12X2 + 8X3 + 10X4 Subject to X1 + X2 + X3 + X4 0 Total Profit Resource 1 Resource 2 Resource 3 Where X1, X2, X3 and X4 represent the number of units of Product 1, Product 2, Product 3 and Product 4 to be manufactured The Excel Solver output for this problem is given below. X1 X2 12 X3 8 X4 10 10 . Variables Objective Function Constraints Constraint 1 Constraint 2 Constraint 3 1 1 1 2 RHS 200 450 300 Used 200 450 275 1 2 1 Slack/Surplus 0 0 oo 1 2 3 1 2 25 Variable X1 X2 X3 X4 OF Value Value 75 125 0 0 2250 Microsoft Excel 16.0 Sensitivity Report Worksheet: [Final Exam Question 3 Excel Answer.xlsx]Sheet1 Report Created: 5/15/2022 5:32:47 PM Variable Cells Cell Name $C$11 X1 Value $C$12 X2 Value $C$13 X3 Value $C$14 X4 Value Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 75 0 10 2 2 125 0 12 18 2 0 -3 8 3 1E+30 0 - 1 10 1 1E+30 Constraints Cell Name $H$6 Constraint 1 Used $H$7 Constraint 2 Used $H$8 Constraint 3 Used Final Shadow Constraint Allowable Allowable Value Price R.H. Si de Increase Decrease 200 9 200 10 50 450 1 450 150 50 275 0 300 1E+30 25 3. (a) Determine the optimal solution and the optimal value and interpret their meanings. (b) Determine the slack (or surplus) value for each constraint and interpret its meaning. 4. (a) What are the ranges of optimality for the profit of Product 1, Product 2, Product 3, and Product 4? (b) Find the shadow prices of the three constraints and interpret their meanings. What are the ranges in which each of these shadow prices is valid? (c) If the profit contribution of Product 1 changes from $10 per unit to $11 per unit, what will be the optimal solution? What will be the new total profit? (Note: Answer this question by using the sensitivity results given above. Do not solve the problem again). (d) Which resource should be obtained in larger quantity to increase the profit most? (Note: Answer this question using the sensitivity results given above. Do not solve the problem again)