document.write( "Question 1205026: The community center needs at least 5 full-time employees and up to 9 part-time volunteers. They want no more than 12 people. Use x to represent the number of full-time employees, and let y represent the number of part-time volunteers. Represent the solution of a system of linear inequality in the situation.
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Algebra.Com's Answer #841627 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "x = number of full-time employees
\n" ); document.write( "y = number of part-time volunteers
\n" ); document.write( "x and y are integers
\n" ); document.write( "They must be nonnegative so $\"x+%3E=+0\"$ and $\"y+%3E=+0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Given facts

The community center needs at least 5 full-time employees.
[They need] up to 9 part-time volunteers.
They want no more than 12 people.

Fact 1 leads to $\"x+%3E=+5\"$
\n" ); document.write( "Fact 2 leads to $\"y+%3C=+9\"$
\n" ); document.write( "Fact 3 means $\"x%2By+%3C=+12\"$ \r
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\n" ); document.write( "\n" ); document.write( "The system of inequalities would be
\n" ); document.write( " $\"system%28x+%3E=+0%2Cy+%3E=+0%2Cx+%3E=+5%2Cy+%3C=+9%2Cx%2By+%3C=+12%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Because $\"x+%3E=+0\"$ and $\"y+%3E=+0\"$ , we focus on the upper right quadrant only.\r
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\n" ); document.write( "\n" ); document.write( "Furthermore, we shade to the right of x = 5 because of $\"x+%3E=+5\"$
\n" ); document.write( "We shade below y = 9 because of $\"y+%3C=+9\"$
\n" ); document.write( "Lastly, shade under $\"x%2By+=12\"$ to take care of $\"x%2By+%3C=+12\"$ \r
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\n" ); document.write( "\n" ); document.write( "The line $\"x%2By+=12\"$ goes through (0,12) and (12,0)\r
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\n" ); document.write( "\n" ); document.write( "All of those regions overlap to form a triangle with these corner points
\n" ); document.write( "A = (5,0)
\n" ); document.write( "B = (5,7)
\n" ); document.write( "C = (12,0)
\n" ); document.write( "Any point inside this region is a solution to the system. Points on the boundary are also solutions as well. Each boundary line is solid due to the \"or equal to\".\r
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\n" ); document.write( "\n" ); document.write( "Desmos graph
\n" ); document.write( "https://www.desmos.com/calculator/bjoscdwkhm
\n" ); document.write( "An example solution in the shaded region is (8,2) marked in blue.
\n" ); document.write( "A non-solution example is (8,6) marked in red.\r
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\n" ); document.write( "\n" ); document.write( "The entire list of solutions is:
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document.write( "(5,7), \r\n" );
document.write( "(5,6), (6,6)\r\n" );
document.write( "(5,5), (6,5), (7,5)\r\n" );
document.write( "(5,4), (6,4), (7,4), (8,4)\r\n" );
document.write( "(5,3), (6,3), (7,3), (8,3), (9,3)\r\n" );
document.write( "(5,2), (6,2), (7,2), (8,2), (9,2), (10,2)\r\n" );
document.write( "(5,1), (6,1), (7,1), (8,1), (9,1), (10,1), (11,1)\r\n" );
document.write( "(5,0), (6,0), (7,0), (8,0), (9,0), (10,0), (11,0), (12,0)\r\n" );
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\n" ); document.write( "There are 36 solution points listed above.
\n" ); document.write( "1 in the first row, 2 in the second, 3 in the third, and so on to get 1+2+3+4+5+6+7+8 = 36\r
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\n" ); document.write( "\n" ); document.write( "If x or y were allowed to be non-integer values, then we'd have infinitely many solutions.
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