
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




















































































































































































































































































































































































































































































































































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?

































