SOLUTION: For a given week, Latoya's Coffee House has available 900 ounces of A grade coffee and 1000 ounces of B grade coffee. These are blended into packages as follows: a deluxe blend tha

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Question 1204141: For a given week, Latoya's Coffee House has available 900 ounces of A grade coffee and 1000 ounces of B grade coffee. These are blended into packages as follows: a deluxe blend that contains 4 ounces of A grade coffee and 8 ounces of B grade coffee, and a special blend that contains 9 ounces of A grade coffee and 5 ounces of B grade coffee. Let x be the number of deluxe blend packages sold. Let y be the number of special bland packages sold. Shade the region corresponding to all values of x and y that satisfy these requirements.
Answer by math_tutor2020(3817) (Show Source):
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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 and are two constraints. It will mean we focus on the upper right quadrant.

Here's a table organizing what the instructions mentioned

Grade A Grade B
Deluxe Blend 4x 8x
Special Blend 9y 5y
Total 900 1000

The first column produces the constraint and the second column gets us

The four contraints we have are:

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

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.