Question

Minimize 6x + 3y
constraints; 4x+3y less than or equal too 24.
4x+y greater than or equal too 16.
x=0 ; y= 0

Answer 1

as i recall you have to sketch the region or at least see where the lines intersect, and then test the corners

Answer 2

i assume the last two are \(x>0,y>0\) yes? the region looks like this
http://www.wolframalpha.com/input/?i=4x%2B3y%3C24+and++4x%2By%3E+16+and+x%3E0+and+y%3E+0

Answer 3

\[4x+3y=24\] and
\[4x+y=16\] intersect at \((\frac{24}{11},\frac{80}{11})\) so you have to check at that point

Answer 4

looks like the other points of intersection are \((0,4)\) and \((0,6)\) so you have to check those as well
is it clear now what you have to do to find the solution ?

Answer 5

at \((0,4)\) you get
\[6x + 3y=6\times 0+3\times 4=12\] at \((0,6)\) you get
\[6x + 3y=6\times 0+3\times 6=18\] and at \((\frac{24}{11},\frac{80}{11})\) you get
\[6x + 3y=6\times \frac{24}{11}+3\times \frac{80}{11}\] whatever that is

Answer 6

@Murry : Need help?

Answer 7

yes!

Answer 8

okay..:D Wait. Lemme draw it..:)

Answer 9

Solve for corner points.