Answer questions 1 to 10 based on the LP formulation given below:

MaxZ=2 X1+3 X2

s.t X1+X2≥3

−3 X1+4 X2≤8

X1≤4

X1 , X2≥0

Que.1 The value of objective function Z is maximized at?

a. (47,177

¿

b. (3, 0)c. (4, 0)d. (4, 5)e. None of the above

Que.2 If the objective function is represented as Z=C1 X1+C2X 2, then for what range of values

of C1 (given C2=3¿ will the solution obtained in question 1 remain optimal?

a. −3≤C1≤∞

b. −3≤C1≤2.2 5

c. −∞≤C1≤2.2 5

d. −2.25≤C1≤∞

e. None of the above

Que.3 If the objective function is represented as Z=C1 X1+C2X 2, then for what range of values

of C2 (given C1=2¿ will the solution obtained in question 1 remain optimal?

a. −2.667≤C2≤0

b. 0≤C2≤2.667

c. 0≤C2≤∞

d. −2.667≤C2≤∞

e. None of the above

Que.4 What is the shadow price of constraint X1+X2≥3 ?

a. 0b. -1c. 4d. 0.75e. None of the above

Que.5 The allowable increase in the R.H.S for which the shadow price of constraint X1+X2≥3 remains valid is?

a. 0b. 1c. Infinityd. 6e. None of the above

Que.6 What is the shadow price of constraint −3 X1+4 X2≤8 ?

a. 4.25b. 0.75c. 0d. Infinitye. None of the above

Que.7 The allowable decrease in the R.H.S for which the shadow price of constraint −3 X1+4 X2≤8 remains valid is?

a. 20b. 8c. Infinityd. 12e. None of the above

Que.8 The allowable increase in the R.H.S for which the shadow price of constraint −3 X1+4 X2≤8 remains valid is?

a. 12b. 8c. Infinityd. 20e. None of the above

Que.9 What is the shadow price of constraint X1≤4 ?

a. 4.25b. 0.25c. 0.75d. 0e. None of the above

Que.10 The allowable decrease in the R.H.S for which the shadow price of constraint X1≤4 remains valid is?

a. 12b. 3.428c. 8d. Infinitye. None of the above

Solution and Answer Key

1.d

2.d

3.c

4.a

5.d

6.b

7.a

8.c

9.a

10.c

The graph for the same has been shown below:

The solver output of the same is as follows:

Variable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease$B$2 4 0 2 1E+30 4.25$C$2 5 0 3 1E+30 3

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease$D$4 9 0 3 6 1E+30$D$5 8 0.75 8 1E+30 20$D$6 4 4.25 4 1E+30 3.428571429