# Linear Programmin maximization problem, shadow price

Consider the following problem.

Maximize Z = 3x1 + 2x2,

subject to

x1 â?¤ 4 (resource 1)

x1 + 3x2 â?¤ 15 (resource 2)

2x1 + x2 â?¤ 10 (resource 3)

and

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.

https://brainmass.com/math/linear-programming/linear-programmin-maximization-problem-shadow-price-357078

#### Solution Preview

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 ...

#### Solution Summary

We solve an LP problem graphically and then find the shadow price for each of the three resources.