It’s attached
OPRE.315.
Direction: Please show all work
. Points related to each problem are marked after
the problem number or problem part.
What is the slope of line 2x +3y – 10= 0?
2) State whether each of the following linear programming problems:
a) has a unique solution;
b) unbounded;
c) infeasible;
d) has multiple optimal solution;
e) or no solution at all.
Note: you still must show works such as graphing, finding feasible region and so on.
i) Max 2x+3y
s.t. x + y 2
2x+3y 9
x 0
A8 y 0
ii) Max 2x+2y
s.t.
x + y 2
x 0
A8 y 0
iii) Max 2x+2y
s.t.
x + y 2
2x+ y 6
x 0
A8 y 0
Consider the following linear programming problem
Max 8X1+9X 2
s.t.
X1 + 6X2 < 60
2 X1 + 3X2 < 60
X1, X2 0
a. Use a graphical technique to show each constraint and the feasible region. Clearly identify the X1 and X 2 values of each vertex.
X2
X1
b. Identify the optimal solution point on your graph. What are the values of X1 and X2 at the optimal solution? What is the value of optimal solution?
c. write the standard form of the system then calculate the values of slack variables?
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