document.write( "Question 251879: Maximize z = 3x + 5y subject to the constraints
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\n" ); document.write( " x ≥ 0, y ≥ 0, y <= 8, x + y ≥ 2, 4x + y <= 12 \n" ); document.write( "

Algebra.Com's Answer #183598 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Start by graphing the constraints:
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\n" ); document.write( "and we get a region bounded by the x-axis, the y-axis and the lines y = 8, x + y = 2 and 4x + y = 12. The maximum (and minimum) values are found at one of the vertices of this region. So we need to find the coordinates of each vertex and then figure out the z for each of these pairs of x and y values. One of the z's will be a maximum value and another will be the minimum value.

\n" ); document.write( "From the graph or by using Algebra we should be able to find that the vertices are: (0, 2), (0, 8), (1, 8), (3, 0), (2, 0). So we take each one of these and find its value for z. The z for one of these points will be the maximum. I'll get you started:
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document.write( "Vertex     z = 3x + 5y\r\n" );
document.write( "(0, 2)     z = 3(0) + 5(2) = 0 + 10 = 10\r\n" );
document.write( "(0, 8)     z = 3(0) + 5(8) = 0 + 40 = 40\r\n" );
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\n" ); document.write( "I'll leave it up to you to finish the other three. \n" ); document.write( "

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