Name:
SA305 – Linear Programming
Asst. Prof. Nelson Uhan
Spring 2016
Quiz 1
Instructions. You have 15 minutes to complete this quiz. You may not use any other materials (e.g., notes, homework,
books).
Problem 1. Consider the following linear program, and its partially sketched constraints:
y
maximize
x + 3y
subject to
x − 2y ≥ −4
(1)
4x + 3y ≤ 17
(2)
4
x≥0
3
y≥0
2
1
-4
-3
-2
-1
1
2
3
4
x
-1
-2
-3
-4
a. (4 points) On the graph above, indicate which lines correspond to the constraints labeled (1) and (2).
b. (4 points) On the graph above, shade in the feasible region.
c. (4 points) On the graph above, draw a line that represents feasible solutions that have a value of 3.
d. (6 points) On the graph above, use the graphical method to determine an optimal solution and the optimal value.
e. (2 points) Looking over your shoulder, Professor I. M. Wright declares to you, “We can clearly change the objective
funcion of this linear program so that the solution x = 2, y = −2 is optimal.” Is he correct? Why or why not?