z=3x-6y,(3,2), (4,8), (8,3), (10,0). What would be the minimum and maximum values obtained for the objective function?

Question

z=3x-6y and the following critical points that would be identified by graphing constraint equations obtaining the shaded area bordered by these points: (3,2), (4,8), (8,3), (10,0). What would be the minimum and maximum values obtained for the objective function?

Answer 1

Your objective function is z, as given. The points you've found are (x, y) pairs. To find the minimum (and maximum) values, plug in each point into your z equation, and figure out which ones give you the lowest (and highest) results.

 

z = 3x - 6y

 

Your first value would be:
(3,2)

z = 3(3) - 6(2) = 9 - 12 = -3

 

Now do the same for the rest.