--%>
Assignment Help - homework help

Sample Questions in Graphical Solution Procedure

Solved problems in Graphical Solution Procedure, sample assignments and homework

Questions: Minimize Z = 10x1 + 4x2

Subject to

3x1 + 2x2 ≥ 60

            7x1 + 2x2 ≥ 84

            3x1 +6x2 ≥ 72

x1 ≥ 0 , x2 ≥ 0

 

Answer

The first constraint 3x1 + 2x2 ≥ 60, can be written in form of equation

3x1 + 2x2 = 60

Place x1 =0, then x2 = 30

Place x2 =0, then x1 = 20

Then the coordinates are (0, 30) and (20, 0)

 

The second constraint 7x1 + 2x2 ≥ 84, can be written in form of equation

7x1 + 2x2 = 84

Place x1 =0, then x2 = 42

Place x2 =0, then x1 = 12

The coordinates then are (0, 42) and (12, 0)

 

The third constraint 3x1 +6x2 ≥ 72, can be written in form of equation

3x1 +6x2 = 72

Place x1 =0, then x2 = 12

Place x2 =0, then x1 = 24

Thus, coordinates are (0, 12) and (24, 0)

 

The graphical presentation is

 

 1485_Graphical Solution Procedure Sample Assignment.png 

 

The corner positions of feasible region are A, B, C and D. Thus the coordinates for the corner points are

A (0, 42)

B (6, 21) (Solve the two equations 7x1 + 2x2 = 84 and 3x1 + 2x2 = 60 to obtain the coordinates)

C (18, 3) Solve the two equations 3x1 +6x2 = 72 and 3x1 + 2x2 = 60 to obtain the coordinates)

D (24, 0)

 

We are given that Min Z = 10x1 + 4x2

At A (0, 42)

Z = 10(0) + 4(42) = 168

 

At B (6, 21)

Z = 10(6) + 4(21) = 144

 

At C (18, 3)

Z = 10(18) + 4(3) = 192

 

At D (24, 0)

Z = 10(24) + 4(0) = 240

 

The minimum value is calculated at the point B. Consequently Min Z = 144 and x1 = 6, x2 = 21

   Related Questions in Basic Statistics

  • Q : Creating Grouped Frequency Distribution

    Creating Grouped Frequency Distribution: A) At first we have to determine the biggest and smallest values. B) Then we have to Calculate the Range = Maximum - Minimum C) Choose the number of classes wished for. This is generally between 5 to 20. D) Find out the class width by dividing the range b

    		•
  • Q : Statistics basic question This week you

    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 : Model Checking Approach Model Checking

    Model Checking Approach: • Specify program model and exhaustively evaluate that model against a speci?cation        –Check that properties hold   

  • Q : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • 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 : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•
  • 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.

    		•
  • Q : Hw An experiment is conducted in which

    An experiment is conducted in which 60 participants each fill out a personality test, but not according to the way they see themselves. Instead, 20 are randomly assigned to fill it out according to the way they think a parent sees them (i.e. how a parent would fill it out to describe the participant

    		•
  • Q : Sample z test and Sample t test A

    A random sample X1, X2, …, Xn is from a normal population with mean µ and variance σ2. If σ is unknown, give a 95% confidence interval of the population mean, and interpret it. Discuss the major diff

    		•
  • 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

    		•