Answer in Microeconomics for ardil #113174

The red thick line shows the gradient of the objective function, the red thin line shows the level line so that the indicated region remains in the region in which the values ​​of the objective function are accepted that are smaller than this.

We see that this function reaches its maximum value at a point with coordinates (0; 8)

“z_{max}=4times 0+8 times 8=64”

“z=3x_1+2x_2 to min”

Arguing in a similar way, we see that this function reaches its minimum value at a point with coordinates (8; 4)

“z_{min}=3times8+2times4=24+8=32”