a) (10 points) What decision variables will you use? Be clear about what values they hold.
b) (10 points) Write the objective of this linear programming problem in terms of the decision variables.
c) (30 points) Use the decision variables to write the inequalities describing Juan's constraints below.
Maximize: | 4 x | + | 8 y | |||
Subject to: | 6 x | + | 1 y | ≥ | 14 | (1) |
5 y | ≤ | 10 | (2) | |||
3 x | + | 2 y | ≤ | 19 | (3) | |
x | ≥ | 0 | (4) | |||
y | ≥ | 0 | (5) |
a) (15 points) Shade in the feasible region for this linear programming problem.
b) (15 points) Find the optimal solution by plugging the coordinates of the corners of the feasible region into the objective function. Circle the corner corresponding to the optimal solution.
c) (10 points) Which constraints are binding?
d) (10 points) What is the slack associated with constraint number (4)?