Expert: Steve Holleran - 5/14/2008

Question
Consider the following linear programming problem:
  Max Z = $15x + $20y
  Subject to :8x + 5y <=  40
         0.4x + y >=  4
        x, y >= 0
Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?  

Answer
Hi Jenna,

Well, I  think I can help with the first part of this one.

When you graph the constraints, the four important points are :

 (0,0)    (5,0)    (0,4)    (10/3, 8/3)

I find that (0,0) gives z = 0

           (5,0) gives Z = 75

           (0,4) gives z = 80

           (10/3 , 8/3) gives z = 103 1/3  so this is the max

I really don't know what the "amount of slack" means.

Hope this was of a little help.

Steve