I need to find the max and min values by evaluating C=2x+y at critical points with restrictions x=0, y=0 and x+y

Question

I need to find the max and min values by evaluating C=2x+y at critical points with restrictions x>=0, y>=0 and x+y<=8  Is min 0 and max 8
Is max 8 and min 0?

anonymous · Answer

$$x+y \le8  ...(1)$$
consider x+y=8
x=0,y=8,point is B (0,8)
y=0,x=8 ,point isA (8,0)
put x=0,y=0 in (1)
$$0+0 \le 8 ,0\le 8,which~ is~ true. also~ x \ge 0,y \ge 0$$
Feasible region is OABO.
Draw.
|dw:1394225858534:dw|
find the value of C at these three points. or plug the values of x and y in C=2x+y
and find where it is maximum and where it is minimum.

anonymous · Answer

so min is 0 and max is 8?