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!!

Re: Linear Programming - Elimination Method help

Quote:

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?

Re: Linear Programming - Elimination Method help