Thread: Linear Programming - Elimination Method help

Hi: This may be slightly more advanced than basic algebra but I think it fits.

I have the following equation:

Maximize Z = 60x + 90y

Subject to:

7x+7y < or = 350
160x+80y > or = 4000
y < or = 25
x > or = 20

This is a maximization / linear programming example where I'd find the feasable region and then determine the optimum solution.

My first step was to sub 0 in for x and y in both equations, getting 25,0 and 50,0 and 0,50 for my coordinates. The constraints of y<or =20 and x > or =0 give me the feasable region but I am having trouble using the substution method to solve for the optimum solution.

Every example I have seen and looked up have been simple numbers where you can either add down, subtract, or multiple by a small amount to get a variable to cancel out. In this situation, 7 does not go into 80 or 160 evenly.

I tried using the LCM and came up with 80, but when I run that number through I end up with 560x = 0, so I know I must be doing something wrong.

How do you handle numbers that do not cancel out evenly?

Thanks!!

Originally Posted by ljj

Hi: This may be slightly more advanced than basic algebra but I think it fits.

I have the following equation:

Maximize Z = 60x + 90y

Subject to:

7x+7y < or = 350
160x+80y > or = 4000
y < or = 25
x > or = 20

This is a maximization / linear programming example where I'd find the feasable region and then determine the optimum solution.

My first step was to sub 0 in for x and y in both equations, getting 25,0 and 50,0 and 0,50 for my coordinates. The constraints of y<or =20 and x > or =0 give me the feasable region but I am having trouble using the substution method to solve for the optimum solution.

Every example I have seen and looked up have been simple numbers where you can either add down, subtract, or multiple by a small amount to get a variable to cancel out. In this situation, 7 does not go into 80 or 160 evenly.

I tried using the LCM and came up with 80, but when I run that number through I end up with 560x = 0, so I know I must be doing something wrong.

How do you handle numbers that do not cancel out evenly?

Thanks!!

Hint: 7 divides 350! The first equation reduces to



Now can you use it for elimination?

Hello, ljj!

The line of [1] has intercepts (50, 0) and (0, 50).
Draw the line and shade the region below the line.

The line of [2] has intercepts (25,0) and (0,50).
Draw the line and shade the region above the line.

The line of [3] is the vertical line:
Draw the line and shade the region to the right of the line.

The line of [4] is the horizontal line:
Draw the line and shade the region below the line.


The critical region looks like this:

Code:

      |
      *
      |**
      | * *   |
      |  *  * |
      |   *   *
      |    * D| *  C
    - + - - * o---o
      |      *|:::::*
      |      Eo:::::::*
      |       |*::::::::*
  - - + - - - + o---------o - -
      |         A         B

The vertices are: .

Test the vertices in the z-function and determine the maximum z.