Question

Exercise 4: Answer both (a) and (b) for full credit. Consider the following LP problem: Maximize Profit Objective Function: $1X1 + $1X2 Subject to: 2X1 + 1X2 s 100 1X, + 2X, s 100 a) What is the optimal solution to this problem? Solve it graphically. b) If a technical breakthrough occurred that raised the profit per unit of X, to $3, would this affect the optimal solution? Show it graphically.

Answer 1

a) The graph of the inequalities is plotted as shown

The optimal solution is the point of intersection shown on the graph

200 (0.100) -200 200 300 400- -100 200

$(X_1,X_2)=(0,100)$

b) If profit of $X_1$ is raised to $3 per unit, the profit maximising objective function becomes

$\$3X_1+\$1X_2$

The constraints however remain same.

The objective function is also depicted on the graph below along with the constraints

200. (0.100) -300 -200 - 100 200 300 400 - 100 -200.
The optimal solution remains at $(X_1,X_2)=(0,100)$ . Hence optimal solution is not changed.