# Thread: Linear Programming Problems? Find the corresponding values of the slack variables.

1. ## Linear Programming Problems? Find the corresponding values of the slack variables.

So i'm not sure where this question would fit within the categories given, but it is a linear programming problem and it is as follows:

Consider the linear programming problem

Maximize z=2x+5y
subject to
2x+3y$\displaystyle \leq$10
5x+y$\displaystyle \leq$12
x+5y $\displaystyle \leq$ 15
x$\displaystyle \geq$0, y$\displaystyle \geq$0

Part (a): verify that x=[1] (this is a vector) is a feasible solution. For part (a) i
[2]
had no problems verifying it but I need it for part (b)

Part (b) For the feasible solution in a, find the corresponding values of the slack variables.

I started setting it up in canonical form but there are three constraints but two items in the vector given in (a) so i'm stuck. I had started adding in the slack variables as in: 2x+3y+u=10 etc.. but I don't know how to do this one when there are three constraints and two items in the vector.

2. Originally Posted by tn11631
So i'm not sure where this question would fit within the categories given, but it is a linear programming problem and it is as follows:

Consider the linear programming problem

Maximize z=2x+5y
subject to
2x+3y$\displaystyle \leq$10
5x+y$\displaystyle \leq$12
x+5y $\displaystyle \leq$ 15
x$\displaystyle \geq$0, y$\displaystyle \geq$0

Part (a): verify that x=[1] (this is a vector) is a feasible solution. For part (a) i
[2]
had no problems verifying it but I need it for part (b)

Part (b) For the feasible solution in a, find the corresponding values of the slack variables.

I started setting it up in canonical form but there are three constraints but two items in the vector given in (a) so i'm stuck. I had started adding in the slack variables as in: 2x+3y+u=10 etc.. but I don't know how to do this one when there are three constraints and two items in the vector.
You have one slack variable for each constraint, write it in terms of x and y (rearrange the constraint equation with the slack variable on the left and every thing else on the right). Now substitute x=1, y=2 into each of these equations...

CB

3. Originally Posted by tn11631
So i'm not sure where this question would fit within the categories given, but it is a linear programming problem and it is as follows:

Consider the linear programming problem

Maximize z=2x+5y
subject to
2x+3y$\displaystyle \leq$10
5x+y$\displaystyle \leq$12
x+5y $\displaystyle \leq$ 15
x$\displaystyle \geq$0, y$\displaystyle \geq$0

Part (a): verify that x=[1] (this is a vector) is a feasible solution. For part (a) i
[2]
had no problems verifying it but I need it for part (b)

Part (b) For the feasible solution in a, find the corresponding values of the slack variables.

I started setting it up in canonical form but there are three constraints but two items in the vector given in (a) so i'm stuck. I had started adding in the slack variables as in: 2x+3y+u=10 etc.. but I don't know how to do this one when there are three constraints and two items in the vector.
You have one equation for each inequality constraint each with a different slack variable. Solve for the slack variable in each and put x=1, y=2 to get the value of the slack variable corresponding to each constraint.

CB

4. Originally Posted by CaptainBlack
You have one equation for each inequality constraint each with a different slack variable. Solve for the slack variable in each and put x=1, y=2 to get the value of the slack variable corresponding to each constraint.

CB
Thats what I was doing on my paper but then I got confused because I had u=10-2x-3y and v=12-5x-y but then what about x+5y$\displaystyle \leq$15? I don't know what to do there because there are only two variables x and y so there should be two slack variables u, and v but then im still left with x+5y$\displaystyle \leq$15. Thanks !

5. Originally Posted by tn11631
Thats what I was doing on my paper but then I got confused because I had u=10-2x-3y and v=12-5x-y but then what about x+5y$\displaystyle \leq$15? I don't know what to do there because there are only two variables x and y so there should be two slack variables u, and v but then im still left with x+5y$\displaystyle \leq$15. Thanks !
$\displaystyle w=15-x-5y$

so at the given point $\displaystyle w=15-1-10=4$

CB

6. Ohh wow don't I feel dumb for missing that maybe too much math for one night. Thanks so much!