Find the minimum value of the region formed by the system of equations and functions below.
y ≥ x ­- 3
y ≤ 6 ­- 2x
2x + y ≥ - ­3
f(x, y) = 3x + 4y
­a. -12
­b. -4.5
c. 9
d. 24

  A.  -12

Step-by-step explanation:

A graph shows the vertices of the feasible region to be (0, 6), (3, 0) and (0, -3). Of these, the one that minimizes f(x, y) is (0, -3). The minimum value is ...

  f(0, -3) = 3·0 + 4(-3) = -12

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Comment on the graph

Here, three regions overlap to form the region where solutions are feasible. By reversing the inequality in each of the constraints, the feasible region shows up on the graph as a white space, making it easier to identify. The corner of the feasible region that minimizes the objective function is the one at the bottom, at (0, -3).