Maximize inequalities help

Question

Maximize

z=4x+6y

 

subject to:

 

x+y≥3

 

y≤5

 

x≤4

 

x≥0,y≥0

Answer 1

Hello Katie -

 

The maximum value is z = 46, with x = 4 and y = 5, given the constraints.

 

There are a few ways to do this, and perhaps the easiest is with a geometric approach. That is a bit difficult to illustrate here, but the idea is to graph the line and the constraints, and see what region is left, and then find values in the region. 

 

Let me know if you need more on this,

 

Ken