A linear programming problem is given as follows: min ? = −4?1 + ?2 Subject to 8?1 + 2?2 ≥ 16 4?1 + 2?2 ≤ 12 ?1 ≤ 6 ?2 ≤ 4 ?1, ?2 ≥ 0
A linear programming problem is given as follows:
min ? = −4?1 + ?2
Subject to 8?1 + 2?2 ≥ 16
4?1 + 2?2 ≤ 12
?1 ≤ 6
?2 ≤ 4
?1, ?2 ≥ 0
I) Find the A, B, C, D, E, F, and G points on the plot below
II) Identify the feasible solution area graphically on the following plot (by shading the
area)
III) Which points are the extreme points
IV) What is the solution of the optimization problem? (x1=?,x2=?,z=?) Show your work
V) Which change will make the problem have multiple optimal solutions? If there is more than one answer, choose all.
a) Increase of the coefficient of ?1 on the objective function to 4
b) Increase of the coefficient of ?1 on the objective function to 2
c) Decrease of the coefficient of ?1 on the objective function to -8
d) Increase of the coefficient of ?2 on the objective function to -8
e) None
VI) If new constraints, ?1≤4 and ?2≤6, are added to the given problem, what effect will be? (choose all the effects)
a) The feasible solution area will be smaller.
b) The feasible solution area will be larger.
c) The given problem becomes infeasible.
d) The optimal point will be changed.
e) The objective value will be decreased.
f) There will be no effect.
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