--%>
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 : Compute two sample standard deviations

    Consider the following data for two independent random samples taken from two normal populations. Sample 1 14 26 20 16 14 18 Sample 2 18 16 8 12 16 14 a) Com

    		•
  • 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 : Building Models Building Models • What

    Building Models • What do we need to know to build a model?– For model checking we need to specify behavior • Consider a simple vending machine – A custome rinserts coins, selects a beverage and receives a can of soda &bul

    		•
  • Q : STATISTICS Question This week you will

    This week you will analyze if women drink more sodas than men.  For the purposes of this Question, assume that in the past there has been no difference.  However, you have seen lots of women drinking sodas the past few months.  You will perform a hypothesis test to determine if women now drink more

    		•
  • Q : Hypothesis homework A sample of 9 days

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evidence that the variance in the numbe

    		•
  • Q : Computers playing games How Computers

    How Computers playing games can be categorized according to different dimensions?

    		•
  • 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 : Principles of data analysis For the

    For the data analysis project, you will address some questions that interest you with the statistical methodology we are learning in class. You choose the questions; you decide how to collect data; you do the analyses. The questions can address almost any topic,

    		•
  • 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 : Statics for each of the following

    for each of the following studies a and b decide whether to reject the null hypothesis that groiups come from identical populations. Use the .01 level. (c) Figure the effects size for each study. (d) ADVANCED TOPIC: Carry out an analysis of variance for study (a) using the strucurtal method.

    		•