#### Operations Research Book Back Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
6 x 1 = 6
1. Maximize: z=3x1+4x2 subject to 2x1+x2≤40, 2x1+5x2≤180, x1,x2≥0 in the LPP, which one of the following is feasible corner point?

(a)

x1=18, x2=24

(b)

x1=15, x2=30

(c)

x1=2.5, x2=35

(d)

x1=20, x2=19

2. A solution which maximizes or minimizes the given LPP is called

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

3. The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤20, x + 2y ≤ 20,x > 0 and y > 0 is

(a)

10

(b)

20

(c)

0

(d)

5

4. In the context of network, which of the following is not correct

(a)

A network is a graphical representation

(b)

A project network cannot have multiple initial and final nodes

(c)

An arrow diagram is essentially a closed network

(d)

An arrow representing an activity may not have a length and shape

5. The objective of network analysis is to

(a)

Minimize total project cost

(b)

Minimize total project duration

(c)

Minimize production delays, interruption and conflicts

(d)

All the above

6. Given an L.P.P maximize Z=2x1+3x2 subject to the constrains x1+x2≤1, 5x1+5x2≥0 and x1≥0, x2≥0 using graphical method, we observe

(a)

No feasible solution

(b)

unique optimum solution

(c)

multiple optimum solution

(d)

none of these

7. 4 x 2 = 8
8. Draw the logic network for the following:
Activities C and D both follow A, activity E follows C, activity F follows D, activity E and F precedes B.

9. Construct a network diagram for the following situation:
A

10. Draw the network for the project whose activities with their relationships are given below:
Activities A,D,E can start simultaneously; B,C>A; G,F>D,C; H>E,F.

11. Construct the network for the projects consisting of various activities and their precedence relationships are as given below:
A, B, C can start simultaneously A<F, E; B<D, C; E, D<G

12. 2 x 3 = 6
13. A soft drink company has two bottling plants C1 and C2. Each plant produces three different soft drinks S1, S2 and S3. The production of the two plants in number of bottles per day are:

 Product Plant C1 C2 S1 3000 1000 S2 1000 1000 S3 2000 6000

A market survey indicates that during the month of April there will be a demand for 24000 bottles of S1, 16000 bottles of S2 and 48000 bottles of S3. The operating costs, per day, of running plants C1 and C2 are respectively Rs.600 and Rs.400. How many days should the firm run each plant in April so that the production cost is minimized while still meeting the market demand? Formulate the above as a linear programming model.

14. Maximize Z = 3x1 + 4x2 subject to x1 – x2 < –1; –x1+x2 < 0 and x1, x2 ≥ 0

15. 2 x 5 = 10
16. A furniture dealer deals only two items viz., tables and chairs. He has to invest Rs.10,000/- and a space to store atmost 60 pieces. A table cost him Rs.500/– and a chair Rs.200/–. He can sell all the items that he buys. He is getting a profit of Rs.50 per table and Rs.15 per chair. Formulate this problem as an LPP, so as to maximize the profit.

17. Solve the following LPP by graphical method Minimize z = 5x1+4x2 Subject to constraints 4x1+ x2 ≥ 40 ; 2x1+3x2 ≥ 90 and x1, x2 > 0.