Using the linear programming output above .

(A) If constraint 1s current right hand side were to decrease by 5 units to go from 40 to 35 and constraint 2s current right hand side were to increase 8 units to go from 30 to 38, would both of their shadow prices still be valid, yes or no? Show detail calculations as part of your explanation for your answer.

(B)Also review calculating the new objective function value from changes and sunk cost vs relevant cost

Different titles are used on different output. There are two different outputs being used below. Dual Price is the same as Shadow Price. Constraint Current Value is the same as Constraint Right hand side. Variable (Opt.) Value is the same as Variable Final Value Objective Coefficient Current Value is the same as Variable Objective Coefficient Objective Function Value = 763.333 Variable Value Reduced Cost X1 13.333 0.000 X2 10.000 0.000 X3 0.000 10.889 Constraint 1 Slack/Surplus 0.000 0.000 23.333 Dual Price -0.778 5.556 0.000 2 3 OBJECTIVE COEFFICIENT RANGES Current Value 31.000 35.000 32.000 Upper Limit No Upper Limit 36.167 42.889 Variable Lower Limit X1 30.000 X2 No Lower Limit X3 No Lower Limit RIGHT HAND SIDE RANGES Constraint Lower Limit 77.647 2 126.000 3 96.667 1 Current Value 90.000 150.000 120.000 Upper Limit 107.143 163.125 No Upper Limit Below is the second software output. Dual Price is the same as Shadow Price. Constraint Current Value is the same as Constraint Right hand side. Variable (Opt.) Value is the same as Variable Final Value Objective Coefficient Current Value is the same as Variable Objective Coefficient Upper Limit and Lower Limit is almost the same as Allowable Increase and Allowable Decrease Changing Cells Cell $B$12 $C$12 Name Variable 1 Variable 2 Final Reduced Value Cost 8.461538462 0 4.615384615 0 Objective Allowable Coefficient Increase 5 7 4 8.5 Allowable Decrease 3.4 2.333333333 Constraints Final Value Shadow Price Constraint Allowable R.H. Side Increase Allowable Decrease Cell SB$15 40 0.538461538 40 110 7 Name constraint 1 Used constraint 2 Used constraint 3 Used $B$16 30 1.307692308 30 30 4.666666667 $B$17 13.07692308 0 12 1.076923077 1E+30