Thread: Matrices

I have a worksheet of these problems, if someone could walk me through this one, I can figure out the rest.

Find the maximum value of C=x+3y on the region determined by the constraints {3x+2y<16
{0<x<4
{0<y<5.

Thanks.

Originally Posted by gretchen

I have a worksheet of these problems, if someone could walk me through this one, I can figure out the rest.

Find the maximum value of C=x+3y on the region determined by the constraints {3x+2y<16
{0<x<4
{0<y<5.

Thanks.

Because x+3y is linear in x and y the maximum value for C occurs at a vertex
of the feasible region defined by the constraints.

The attachment shows the feasible region defined by the constraints and the
coordinates of the vertices.

For each vertex evaluate x+3y, and the one that gives the largest of these
values is the maximum value that C can take in the feasible region.

RonL

So, the maximum value would be:

C=x+3y
C=2+3(5)
C=2+15
C=17

Right?

Originally Posted by gretchen

So, the maximum value would be:

C=x+3y
C=2+3(5)
C=2+15
C=17

Right?

Yes.

The values at the vertices are:

(0,0): C=0
(0,5): C=15
(2,5): C=17
(4,2): C=10
(4,0): C=4

RonL