--%>
Assignment Help - homework help

Get Solved LP Problems

Solve Linear Programming Questions

A producer manufactures 3 models (I, II and III) of a particular product. He uses 2 raw materials A and B of which 4000 and 6000 units respectively are obtainable. The raw materials per unit of 3 models are listed below.

Raw materials

I

II

III

A

2

3

5

B

4

2

7

The labour time for each unit of model I is two times that of model II and thrice that of model III. The whole labour force of factory can manufacture an equivalent of 2500 units of model I. A model survey specifies that the minimum demand of 3 models is 500, 500 and 375 units correspondingly. However the ratio of number of units manufactured must be equal to 3:2:5. Suppose that gains per unit of model are 60, 40 and 100 correspondingly. Develop a LPP.

 

Answer

Assume

x1 - number of units of model I

     x2 - number of units of model II

     x3 - number of units of model III

 

 

 Raw materials

I

II

III

Availability

A

2

3

5

4000

B

4

2

7

6000

Profit

60

40

100

 

 

x1 + 1/2x2 + 1/3x3 ≤ 2500                                                       Labour time

 

x1 ≥ 500, x2 ≥ 500, x3 ≥ 375                                                    Minimum demand

 

The given ratio is x1: x2: x3 = 3: 2: 5

x1 / 3 = x2 / 2 = x3 / 5 = k

x1 = 3k; x2 = 2k; x3 = 5k

x2 = 2k → k = x2 / 2

So x1 = 3 x2 / 2 → 2x1 = 3x2

Likewise 2x3 = 5x2

 

Maximize Z= 60x1 + 40x2 + 100x3

Subject to 2x1 + 3x2 + 5x3 ≤ 4000

                  4x1 + 2x2 + 7x3 ≤ 6000

x1 + 1/2x2 + 1/3x3 ≤ 2500

2 x1 = 3x2

2 x3 = 5x2

& x1 ≥ 500, x2 ≥ 500, x3 ≥ 375

 

   Related Questions in Basic Statistics

  • Q : Data Description 1. If the mean number

    1. If the mean number of hours of television watched by teenagers per week is 12 with a standard deviation of 2 hours, what proportion of teenagers watch 16 to 18 hours of TV a week? (Assume a normal distribution.) A. 2.1% B. 4.5% C. 0.3% D. 4.2% 2. The probability of an offender having a s

    		•
  • Q : MANOVA and Reflection Activity

    Activity 10:   MANOVA and Reflection   4Comparison of Multiple Outcome Variables This activity introduces you to a very common technique - MANOVA. MANOVA is simply an extension of an ANOV

    		•
  • Q : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • Q : Program Evaluation and Review

    Program Evaluation and Review Technique (PERT) A) Developed by US Navy and a consulting firm in 1958 for the Polaris submarine project. B) Technique as for CPM method, but acti

    		•
  • Q : What is Forced Flow Law Forced Flow Law

    Forced Flow Law: • The forced flow law captures the relationship between the various components in the system. It states that the throughputs or flows, in all parts of a system must be proportional t

    		•
  • Q : Report on Simple Random Sampling with

    One of my friend has a problem on simple random sampling. Can someone provide a complete Report on Simple Random Sampling with or without replacement?

    		•
  • Q : Quantities in a queuing system

    Quantities in a queuing system: A: Count of

    		•
  • Q : State the hypotheses At Western

    At Western University the historical mean of scholarship examination score for freshman applications is 900. Population standard deviation is assumed to be known as 180. Each year, the assistant dean uses a sample of applications to determine whether the mean ex

    		•
  • Q : Get Solved LP Problems Solve Linear

    Solve Linear Programming Questions A producer manufactures 3 models (I, II and III) of a particular product. He uses 2 raw materials A and B of which 4000 and 6000 units respectively are obtainable. The raw materials per unit of 3

    		•
  • Q : Designing a system What are the

    What are the questions that comes into mind when designing a system?

    		•