Consider the following problem.
Maximize Z = 3x1 + 2x2,
x1 â?¤ 4 (resource 1)
x1 + 3x2 â?¤ 15 (resource 2)
2x1 + x2 â?¤ 10 (resource 3)
x1 â?¥ 0, x2 â?¥ 0,
where Z measures the profit in dollars from the two activities and the right-hand sides are the number of units available of the respective resources.
(a) Use the graphical method to solve this model.
(b) Use graphical analysis to determine the shadow price for each of these resources by solving again after increasing the amount of the resource available by 1.
First, we solve the original problem and find the optimal value of the objective function (see the first picture). The easiest way to graph the feasible region is to graph the boundary lines (usually, by finding their ...
We solve an LP problem graphically and then find the shadow price for each of the three resources.