Question 1204141
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x = number of deluxe blend packages sold
y = number of special blend packages sold
x and y are nonnegative whole numbers which means {{{x >= 0}}} and {{{y >= 0}}} are two constraints. It will mean we focus on the upper right quadrant.


Here's a table organizing what the instructions mentioned
<table border = "1" cellpadding = "5"><tr><td></td><td>Grade A</td><td>Grade B</td></tr><tr><td>Deluxe Blend</td><td>4x</td><td>8x</td></tr><tr><td>Special Blend</td><td>9y</td><td>5y</td></tr><tr><td>Total</td><td>900</td><td>1000</td></tr></table>


The first column produces the constraint {{{4x+9y <= 900}}}	and the second column gets us {{{8x+5y <= 1000}}}



The four contraints we have are:
{{{system(x >= 0,y >= 0,4x+9y <= 900,8x+5y <= 1000)}}}


Once again we're focused on the upper right quadrant only.


In this quadrant, we'll shade below the boundary lines 4x+9y = 900 and 8x+5y = 1000 to get the final answer that is shown here
{{{
drawing(400,400,-40,240,-40,240,
graph(400,400,-40,240,-40,240,-1000,(900-4x)/9,(1000-8x)/5),

locate(30,30,matrix(1,2,"shaded","region"))
)
}}}
These boundary lines are solid because of the "or equal to" portions of the inequality signs. It will mean points on the boundary are valid solutions. The boundary points must be adjacent to the interior shaded region.


The green line represents 4x+9y = 900. That line goes through (0,100) and (225,0)
The blue line represents 8x+5y = 1000. That line goes through (0,200) and (125,0)


GeoGebra and Desmos are great graphing tools for this sort of problem. 
There are other online calculators that can offer similar capabilities.
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