Question

NEED THE ANSWER ASAP PLEASE

Answer 1

It's a linear program; the extrema will be at the corners.

Let's enumerate them.  4 choose 2 gives 6 possible meets of 4 lines.  One pair are parallel, down to five to try.

4x-y=1 intersects x=0 at y=-1, outside the domain y≥0.

4x-y=1 intersects y=0 at x=1/4, (1/4, 0)

4x-y=1 intersects x=5 at y=19, (5,19)

(0,0) is outside the domain 4(0)-0=0 which isn't ≥1.

(5,0) is a valid corner.

It's a triangular domain.  Three points to try,

C(1/4,0) = 6(1/4) + 2(0) = 3/2

C(5,19) = 6(5) + 2(19) = 68

C(5,0) = 6(5) + 2(0) = 30

Answer: Maximum C=68 at (x,y)=(5,19)