For the preceding problem, determine the coordinates ofeach feasible corner point us-
ing the original objective function. Then, determine the profit at each of those corner
points. Use that information to identify the optimal solution.
Given this linear programming model:
maximize Z = 10x1 +16 x2 (profit)
subject to
A 8 x1 + 20 x2 ?120
B 25 x1 + 20 x2 ? 200
x1, x2 ?0
Solution
I'm going to let x1be the independent variable (x axis) while x2will be the
dependent variable (y) The constraints: x1>0, and x 2>0 limit your graph to the I Quadrant, they
represent the x and y axes. We need to rewrite the other two constraints so the x2= f(x1), then
they can be graphed. 8x1+ 20x2< 120 ?? x1< ( - 20x2+ 120)/8 ?? x1< - 5/2x2 + 15 Graph that
using a broken line, then shade the region below your graph. 25x1+ 20x2< 200 ?? x1< ( -20x2+
200)/25 ?? x 1< -4/5x 2+ 8 Graph with broken line, shade region below! The figure made by the
axes and your two lines (the constraints) makes a quadrilateral, identify the 4 points of
intersection of your constraint lines (the corners). Plug those points into your Profit equation (Z
= 10x1+ 16x2) and identify which set of points gives you the maximum profit.