Answer the next three questions using the linear programming output above

(A) If the current value of the coefficient with the variable X1 decreases by 2 units to go from 31 to 29, would the optimal value for X1 (13.333) still be valid, yes or no? Use words and numbers to explain your answer.

(B) If the current value of the coefficient with the variable X2 increases by 1 unit to go from 35 to 36, would the optimal value for X2 (10) still be valid, yes or no? Use words and numbers to explain your answer.

(C) If the current value of the right hand side for constraint 1 increases by 10 units to go from 90 to 100, would the corresponding dual price of (-0.778) still be valid, yes or no? Use words and numbers to explain your answer.

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