# Or Assignment

**Topics:**Operations research, Cumulative distribution function, Linear programming

**Pages:**10 (1830 words)

**Published:**January 1, 2013

Ans.

Let x1 and x2 be the number of dolls produced per day of type A and B respectively.

Let the doll A require “t” hrs to make.

So the doll B would require “2t” hours to make.

So the total time to manufacture x1 & x2 dolls should not exceed 1000 per day. Therefore,

x1 + 2x2 ≤ 1000 (time constrain).

Other constrains are:

x1 + x2 ≤ 1000 (Plastic constrain).

x2 ≤ 500 (Dress constrain).

And the non-negative constrains are

x1 ≥0, x2 ≥0

Maximize the profit function:

p = 3x1 + 5x2

2. What are the advantages of Linear programming techniques?

Ans. Advantages—

1. The linear programming technique helps to make the best possible use of available productive resources (such as time, labour, machines etc.)

2. It improves the quality of decisions. The individual who makes use of linear programming methods becomes more objective than subjective.

3. It also helps in providing better tools for adjustment to meet changing conditions.

4. It highlights the bottlenecks in the production processes.

5. As the problem is linear in nature the computational power required is less compared to non-linear methods. Therefore, large problems like optimization of an entire refinery can be performed using LP technique using desk top computers.

3. Solve the following Assignment Problem

|Operations | | | | | | |M1 |M2 |M3 |M4 | |O1 |10 |15 |12 |11 | |O2 |9 |10 |9 |12 | |O3 |15 |16 |16 |17 |

Ans:

1) Introducing the dummy row

|Operations | | | | | | |M1 |M2 |M3 |M4 | |O1 |10 |15 |12 |11 | |O2 |9 |10 |9 |12 | |O3 |15 |16 |16 |17 | |O4 |0 |0 |0 |0 |

2) Row reduced matrix

|Operations | | | | | | |M1 |M2 |M3 |M4 | |O1 |0 |5 |2 |1 | |O2 |0 |1 |0 |3 | |O3 |0 |1 |1 |2 | |O4 |0 |0 |0 |0 |

3) Column reduced matrix

Table same as step 2.

4) Draw the minimum number of straight lines needed to cover all zeros. Since three lines suffice, the solution is not optimal. (There are four operators, i.e. O1, O2, O3 and O4 to be assigned so need minimum four line)

|Operations | | | | | | |M1 |M2 |M3 |M4 | |O1 |0 |5 |2 |1 | |O2 |0 |1 |0 |3 | |O3 |0 |1...

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