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Homework 2 Linear Programming
Your Score:
Han Solo and Chewbacca fly the Millennium Falcon.
They are considering a trip to Bespin.
They can carry passengers and cargo containers.
Let
x
be the number of passengers and
y
be the number of containers.
1) Han wants to carry at least 15 goods containers.
2) He also wants to carry at least 5 passengers.
3) Each passenger requires 3m
2
and each container requires 1m
2
of cargo space.
The total amount of cargo space available is 60m
2
.
4) Finally, Han wants the number of containers to be at least twice the number of passengers.
Translate these conditions into inequalities below. Use "geq" for
≥ and "leq" for ≤.
1)
x
+
y
2)
x
+
y
3)
x
+
y
4)
x
+
y
Han and Chewbacca estimate they will make a profit of $5600 for each passenger and $800 for each container shipped.
Enter the objective function below:
P =
x +
y
Enter two points for each constraint line to generate a plot in the window below.
You should choose points which clearly show the region formed by the constraints.
Constraint 1
x
y
Point 1
Point2
Constraint 2
x
y
Point 1
Point2
Constraint 3
x
y
Point 1
Point 2
Constraint 4
x
y
Point 1
Point 2
[No canvas support]
Starting with the corner point nearest the origin,
(0, 0)
, enter the corner points in clockwise order:
Give your answers rounded to 2 decinmal places.
Calculate "
P
" based on your
rounded
answers.
Feasible Region Corner Points
x
y
P
Corner Point 1
Corner Point 2
Corner Point 3
Corner Point 4
The objective function is maximised at corner point number:
How many passengers should be shipped to maximise profits?
How many containers should be shipped to maximise profits?
What is the maximum profit for Han and Chewbacca?
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