Question 150196
use the graphical method to solve each linear programming. 
Maximize to subject: z = 2x + 4y 
3x + 2y _< 12
5x + y _> 5
x_>0
y_>0
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Since both x and y are >= 0 your solutions are in the 1st quadrant.
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Graph y = (-3/2)x + 12 and shade the half-plane below (<) it in the 1st quadrant.
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Graph y = -5x + 5 and shade the half-plane above (>)it in the 1st and under
the previous line.
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{{{graph(400,300,-10,10,-10,15,(-3/2)x+12,-5x+5)}}}
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Find the vertices of the resulting geometric figure (quadrangle).
(0,12)(0,5)(8,0)(1,0)
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Substitute each pair into your objective function to find which x/y pair gives the maximum z value.
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Cheers,
Stan H.