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## Homework Statement

This was from a test I took today:

Maximize z = 4x + y subject to:

4x + 2y = 7

3x + 2y >= 6

4x + 2y <= 8

1.Graphically solve and find x y and z

2.What are the range of values for c1 (Coefficients of x) so that the solution remains optimal.

## Homework Equations

## The Attempt at a Solution

I graphically solved and found x = 1, y = 1.5, and z = 5.5. The optimal solution is the intersection of these two constraints:

4x + 2y = 7

3x + 2y >= 6

For the c1 & c2 I am running into some confusion and I am not sure why. I am assuming, because he didn't specify, that the c1 and c2 are referring to the objective function coefficients and I am finding the range of values where the solution is still optimal.

Normally to do this you find the slope of the isoprofit line which is -c1/c2 and say that it needs to be bound between the slope of the two intersecting lines.

Slope of (4x + 2y = 7) is -2

Slope of (3x + 2y >= 6) is -3/2

For c1: -2<= -c1/1 <= -3/2

Therefore: 3/2<= c1 <= 2

This answer makes no sense at all since the solution is already optimal and the coefficient is 4...

Any advice on where I am messed up would be great!