Question 536569: Need help on this
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
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! We want to plot the boundaries of the feasibility region, and find their intersection points.
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).
Another boundary is the horizontal line y=45 (y cannot exceed 45).
 is a line (in blue in the drawing below) that intersects the x- and y-axes at the points where
 -->  and
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Where it intersects y=45,
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The feasibility region can be represented as the trapezoid OABC below.
 O=(0,0) A=(0,45) B=(30,45) C=(84,0)
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?
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