document.write( "Question 536569: Need help on this\r
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\n" ); document.write( "\n" ); document.write( "given the profit statement and constraints of a linear programming problem, find the corner points of the feasible set. Maximize P= 6x + 5y Constraints 5x + 6y ≤ 420 x ≤ 60 y ≤ 45 x≥ 0 y≥ 0 \n" ); document.write( "

Algebra.Com's Answer #352509 by KMST(5328) $\"\"$ $\"About$

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We want to plot the boundaries of the feasibility region, and find their intersection points.
\n" ); document.write( "Obviously x and y are defined so that they cannot be negative, because two of the boundaries are the x- and y-axes (y=0 and x=0).
\n" ); document.write( "Another boundary is the horizontal line y=45 (y cannot exceed 45).
\n" ); document.write( " $\"5x%2B6y=420\"$ is a line (in blue in the drawing below) that intersects the x- and y-axes at the points where
\n" ); document.write( " $\"5x=420\"$ --> $\"x=84\"$ and
\n" ); document.write( " $\"6y=420\"$ --> $\"y=70\"$
\n" ); document.write( "Where it intersects y=45,
\n" ); document.write( " $\"5x%2B6%2A45=420\"$ --> $\"x=30\"$
\n" ); document.write( "The feasibility region can be represented as the trapezoid OABC below.
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O=(0,0) A=(0,45) B=(30,45) C=(84,0)
\n" ); document.write( "For each value of P, P= 6x + 5y will be a straight line. Different values of P will produce parallel lines. As you increase P, the line will move until it reaches a boundary point or a boundary line. It is obvious that point O gives P=0, and that point B will give a greater P than point A. If you calculate P for the coordinates of points B and C, you will find the maximum. I can see that it will be at a point, and not along the blue line, because the P= 6x + 5y lines have a different (steeper) slope than the blue line. In fact, I can even see where the maximum will be, without calculating. Can you? \n" ); document.write( "

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