Operations Research Answers

Consider the following primal problem;

minimize x₀=20x₁+30x₂+50x₃+40x₄

subject to:

4x₁+6x₂+x₃+2x₄≥12

2x₁+x₂+6x₃+5x₄≥14

x₁+2x₂+4x₃+3x₄≥8

x_i≥0,i=1,2,3,4

Use simplex method to solve the dual of the above primal problem

Briefly explain artificial variables/slack variables technique in solving a linear programming

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 given in the table below.

clients

1 2 3 4 5

A 30 37 40 28 40

B 40 24 27 21 36

Salesmen 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 savings the company can achieve from the allocations

A farmer has 50 ha of land on which to plant maize and beans. He has a workforce of 150 laborers and it takes 4 laborers to work on 1 ha of maize and 2 laborers to work on 1 ha of beans . He has a capital of $4500 and 1 ha of maize requires $50 to cultivate while 1 ha of beans requires $100 to cultivate. Suppose that the farmer wishes to maximize profit and the profit per ha is $30 for maize and $40 for beans. Set up a linear programming problem and solve it graphically

identify the three conditions that a critical path must satisfy

Mr odongo is an inventory manager for office supplies in a large office supply warehouse.

The annual demand for paper punches is 20000 units. The ordering cost is $100 per order and carrying(holding) cost is $5 per unit per year. Determine the expected ordering quantity and the fixed order

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