Answer:
Option b (4,1)
Step-by-step explanation:
The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function [tex]f(x, y) = 8x + 8y[/tex]
The minimum points are found in the lower vertices of the region.
These vertices are found by equating the equations of the lines::
[tex]3x+2y=14\\-5x +5y=10[/tex]
-------------------
[tex]x = 2\\y = 4[/tex]
[tex]-8x + 3y = -29\\3x + 2y = 14[/tex]
---------------------
[tex]x = 4\\y = 1[/tex]
The lower vertices are:
(4, 1) (2, 4)
Now we substitute both points in the objective function to see which of them we get the lowest value of [tex]f(x, y)[/tex]
[tex]f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48[/tex]
Then the value that minimizes f(x, y) is (4,1).
Option b
