Min C = 5x - 2y

[Guest]

Min C = 5x - 2y

Subject to:

[tex]x+y\ge8[/tex]
[tex]x\ge4[/tex]
[tex]y\ge3[/tex]

Thanks!

[Guest]

c = 5(x+y)-7y=5*8-7*3=40-21=19
So min C is 19

[Guest]

This is a very simple "linear programming" problem. The target function, 5x- 2y, is linear and the given region, bounded by [tex]x+ y\ge 8[/tex], [tex]x\ge 4[/tex], [tex]y\ge 3[/tex], is convex.

The basic rule for such a problem is that any maximum or minimum must occur at a 'corner'. The line x= 4 crosses the line x+ y= 8 at (4, 4). At that point, 5x- 2y= 5(4)- 2(4)= 20- 8= 12. The line y= 3 crosses x+ y= 8 at (5, 3). At that point, 5x- 2y= 5(5)- 2(3)= 25- 6= 19. The smaller of those is 12 so the minimum value of 5x- 2y is 12, not 19.