Operations Research Answers

Entire queuing can be described by customers behaviour as one of its components. Explain briefly the customers behaviour giving examples in each

Find the dual program of the following linear programming problem

maximize z=5x₁-2x₂

subject to:

3x₁+2x₂ ≥16

x₁-x₂≤4

x₁≥5

x₁≥0, x₂ is unconstrained

Use simplex method to maximize 𝑓 = 3𝑥 + 5𝑦 + 4𝑧 subject to the conditions 2𝑥 + 3𝑦 ≤ 18 2𝑥 + 5𝑦 ≤ 10 3𝑥 + 2𝑦 + 4𝑧 ≤ 15 and 𝑥, 𝑦, 𝑧 ≥ 0.

A company has fixed funds to undertake three projects through contractors. Five contractors have already applied to do the job and each has submitted a quotation for each project from which the company has estimated the saving associated with allocating a given project to a specific contractor. The figures are given in the table below and the company’s policy is to give one project per contractor

. Project

Contractor 1 2 3

A 1020 1080 1050

B 1500 1410 1050

C 1110 750 1050

D 1080 1020 1080

E 1470 1290 1590

Determine who should be assigned which project and the maximum saving the company can make.

) Five applicants are competing for four jobs . The scores from aptitude tests related to the four vacancies are given below. It is believed the tests measure an applicant possible performance in the job.

JOBS

APPLICANTS 1 2 3 4

A 18 15 12 25

B 9 11 10 15

C 12 10 14 16

D 9 10 10 21

E 14 18 26 26

Determine who should be assigned which job in order to maximize overall output

A company has 5 salesmen and 5 customers to attend to on a particular day. The company has estimated the savings in dollars associated with assigning a particular salesman to a specific client. These estimates are as given in the table below

Clients

1 2 3 4 5

A 30 37 40 28 40

Salesmen B 40 24 27 21 36

C 40 32 33 30 35

D 25 38 40 36 36

E 29 62 41 34 39

Determine who should be assigned which client and the maximum profit the company can achieve from the allocations

A small project is composed of 7 activities whose time estimates in weeks are listed below:

Activity Predecessors Optimistic Most likely Pessimistic

A - 1 2 4

B - 5 6 7

C - 2 4 5

D A 1 3 4

E C 4 5 7

F A 3 4 5

G B,D,E 1 2 3

i) Draw the network.

ii) Calculate the expected duration and variance of every task.

iii) Determine the critical path.

iv) Calculate the expected project duration and the variance of the project duration based on network analysis.

v) Calculate the probability that the project will be completed on or before a deadline of 10 weeks

. A tailor has the following material available: 16 sq. yd. cotton, 11 sq. yd. silk and 15 sq. yd. wool. A suit requires 2 sq. yd. cotton, 1 sq. yd. silk and 1 sq. yd. wool. A gown requires 1 sq. yd. cotton, 2 sq. td. Silk and 3 sq. yd. wool. If a suit sells for Rs. 300/- and a gown for Rs. 500/-, how many of each garment should the tailor mak to obtain the maximum amount of profit?

 Explain ways in which the CPM type of networks differ from PERT networks