Question 348482
Graph each line.
{{{x+y=18}}}
{{{y=-x+18}}}
{{{graph(300,300,-2,16,-2,18,-x+18)}}}
The region of interest is the shaded region,
*[invoke plot_any_inequality "y>=-x+18", -2,16, -2, 18, 300, 300]

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Find the intersection between the green line and the red line.
{{{(1/2)x+10=-x+18}}}
{{{x+20=-2x+36}}}
{{{3x=16}}}
{{{x=16/3}}
{{{y=-16/3+54/3=38/3}}}
(16/3,38/3)
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{{{drawing(300,300,-2,16,-2,18,grid(1),circle(16/3,38/3,0.3),graph(300,300,-2,16,-2,18,-x+18,(1/2)x+10))}}}
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{{{5x-y=53}}}
{{{y=5x-53}}}
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Find the intersection between the blue line and the red line.
{{{5x-53=-x+18}}}
{{{6x=71}}}
{{{x=71/6}}}
Then
{{{y=-71/6+108/6=37/6}}}
(71/6,37/6)
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Find the intersection between the blue line and the green line.
{{{5x-53=(1/2)x+10}}}
{{{10x-106=x+20}}}
{{{9x=126}}}
{{{x=14}}}
Then
{{{y=(1/2)14+10}}}
{{{y=17}}}
(14,17)
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{{{drawing(300,300,-2,16,-2,18,grid(1),circle(14,17,0.3),circle(16/3,38/3,0.3),circle(71/6,37/6,0.3),graph(300,300,-2,16,-2,18,-x+18,(1/2)x+10,5x-53))}}}
So the 3 vertices are :
(16/3,38/3)
(71/6,37/6)
(14,17)
Find the value of P=-7x-4y at each vertex.
I will do one, you do the rest.
(14,17):{{{P=-7x-4y=-7(14)-4(17)=-98-68=-166}}}