Question

For the following, graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. + ≤ 3 + 2 ≤ 4 ≥ 0, ≥ 0(, ) = −3 − 4x

Answer 1

First we have to graph the area of interest

The area of interes is marked with purple color.

The vertices of such area are:

(0,0)

(0,3)

(2,1)

(3,0)

Now to find the minumum and maximum values of the function we evaluate the vertices in the function:

f(0,0)=0

f(0,3)=-3*3=-9

f(2,1)=-3(1)-4(2)=-11

f(3,0)=-4*3=-12

Finally we conclude that the maximum value is 0 and the minimum value is -12.