--%>
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 : Safety and Liveness in Model Checking

    Safety and Liveness in Model Checking Approach; •? Safety: Nothing bad happens •? Liveness: Something good happens •? Model checking is especially good at verifying safety and liveness properties    –?Concurrency i

    		•
  • Q : Explain Service times Service times: A)

    Service times:A) In most cases, servicing a request takes a “short” time, but in a few occasions requests take much longer.B) The probability of completing a service request by time t, is independent of how much tim

    		•
  • Q : Develop the most appropriate regression

    Predicting Courier Costs The law firm of Adams, Babcock, and Connors is located in the Dallas-Fort metroplex.  Randall Adams is the senior and founding partner of the firm.  John Babcock has been a partne

    		•
  • Q : Compare the test results The grade

    The grade point averages of 61 students who completed a college course in financial accounting have a standard deviation of .790. The grade point averages of 17 students who dropped out of the same course have a standard deviation of .940. Do the data indicate a

    		•
  • Q : Regression Analysis 1. A planning

    1. A planning official in the Texas Department of Community Affairs, which works in the office next to you, has a problem. He has been handed a data set from his boss that includes the costs involved in developing local land use plans for communities wi

    		•
  • Q : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • 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 : Define Service Demand Law

    Service Demand Law:• Dk = SKVK, Average time spent by a typical request obtaining service from resource k• DK = (ρk/X

    		•
  • 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 : Computing Average revenue using

    Can anyone help me in the illustrated problem? The airport branch of a car rental company maintains a fleet of 50 SUVs. The inter-arrival time between the requests for an SUV is 2.4 hrs, on an average, with a standard deviation of 2.4 hrs. There is no indication of a

    		•