--%>
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 : 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 : 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 : Define SPIN simulation modes SPIN: •

    SPIN: • SPIN generates C program that is the model checker – The pan verifier • Process Analyzer – Run the pan executable to do the model check

    		•
  • Q : Point of estimate standing data se to

    standing data se to develop a point of estimate

    		•
  • Q : FIN512 Entrepreneurial Finance Chapter

      Chapter 6: Discussion Question: #4 p. 223  It is usually easier to forecast sales for a seasoned firm contrast to an early-stage venture because an early-stage venture has limited access to bank credit lines, sho

    		•
  • 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 : 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 : Correlation analysis and the regression

    1).  When you take out a mortgage, there are many different kinds of costs.  Usually the two largest are the interest rate (annual percentage that determines the size of your monthly payment) and the loan fee (a one-time percentage charged to you at the time

    		•
  • 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 : 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

    		•