--%>
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 : 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 : Cumulative Frequency and Relative

    Explain differences between Cumulative Frequency and Relative Frequency?

    		•
  • Q : Decision Variables Determine Decision

    Determine Decision Variables: Let X1 be the number of private homes to be inspectedLet X2 be the number of office buildings to be inspect

    		•
  • Q : Help An experiment is conducted in

    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 : Computers playing games How Computers

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

    		•
  • 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 : 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 : Probability how can i calculate

    how can i calculate cumulative probabilities of survival

    		•
  • Q : Problems on ANOVA We are going to

    We are going to simulate an experiment where we are trying to see whether any of the four automated systems (labeled A, B, C, and D) that we use to produce our root beer result in a different specific gravity than any of the other systems. For this example, we would l

    		•