Question
For the problem, determine the coordinates of each feasible corner point using 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 * 10 x1 * 16 x2 (profit)
subject to
A 8 x1 * 20 x2 * 120
B 25 x1 * 20 x2 * 200
x1, x2 * 0
Explanation / Answer
let x be the independent variable (x axis) while xwill be the dependent variable (y) The constraints: x >0, and x >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 x= f(x ), then they can be graphed. 8x + 20x< 120 x < ( - 20x+ 120)/8 x < - 5/2x + 15 Graph that using a broken line, then shade the region below your graph. 25x + 20x< 200 x < ( -20x+ 200)/25 x < -4/5x + 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 = 10x + 16x) and identify which set of points gives you the maximum profit.