dcc3038026
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Linear programming: 2x+3y<=12, 2x+y<=8, x,y>=0, subject to
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mmm4444bot
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Re: Linear programming
Hi DCC:
Graph the four inequalities; the region where all four overlap forms a polygon. The (x, y) solution is the coordinates of whichever vertex gives the greatest value for z.
Since x and y are both non-negative, the vertices will all be located on either of the positive axes or in the first quadrant.
So actually, you only need to graph the two lines
2x + 3y = 12
2x + y = 8
and then feed the coordinates of the intersection point, the y-intercept closest to the origin, and the x-intercept closest to the origin into the formula for z to discover which xy-coordinates yield the greatest value. (These three vertices plus the origin define the polygon.)
Click HERE for a bunch of examples of this procedure.
Let us know if you need more help. PLEASE show your work and try to explain what you're hung-up over.
Cheers,
~ Mark
Hi DCC:
Graph the four inequalities; the region where all four overlap forms a polygon. The (x, y) solution is the coordinates of whichever vertex gives the greatest value for z.
Since x and y are both non-negative, the vertices will all be located on either of the positive axes or in the first quadrant.
So actually, you only need to graph the two lines
2x + 3y = 12
2x + y = 8
and then feed the coordinates of the intersection point, the y-intercept closest to the origin, and the x-intercept closest to the origin into the formula for z to discover which xy-coordinates yield the greatest value. (These three vertices plus the origin define the polygon.)
Click HERE for a bunch of examples of this procedure.
Let us know if you need more help. PLEASE show your work and try to explain what you're hung-up over.
Cheers,
~ Mark