Question 540293: Can you help me with the constraints on this linear programming question?
A tourist agency can sell up to 1200 travel packages for a football game. The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight. The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers. The agency can locate no more than 10 planes for the travel packages. Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.
Please and Thank You.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A tourist agency can sell up to 1200 travel packages for a football game.
The packages include airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-stop flight.
The nonstop flight can carry up to 150 passengers, and the two-stop flight can carry up to 100 passengers.
The agency can locate no more than 10 planes for the travel packages.
Each package with a nonstop flight sells for $1200, and each package with a two-stop flight sells for $900.
Assuming each plane will carry the maximum number of passengers, find the maximum revenue for the agency.
:
Let x = number of 150 passenger planes
Let y = number of 100 passenger planes
:
Number of airplanes:
x + y =< 10
Put in the general (y=) form, to plot on a graph
y =< 10 - x; (purple line)
:
Number of travel packages sold:
150x + 100y =< 1200
100y =< 1200 - 150x
y =< 1200/100 - (150/100)x
y =< 12 - 1.5x; (green line)
:
The graph:
:
Feasibility region is at or below the purple or green lines whichever is lowest
:
The vertices:
x = 8, y = 0
x = 0, y = 10
Solve the two equation system to find the other vertici
150x + 100y = 1200
Simplify, divide by 100
1.5x + y = 12
x + y = 10
----------------subtract, find x
.5x = 2
x = 2/.5
x = 4
:
Find y:
4 + y = 10
y = 6
The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes
:
Revenue:
4*150*1200 = $720,000
6*100*900 = $540,000
--------------------
total is $1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes
But
Max revenue would be 8 full 150 pass planes, forget the 100 pass planes
8 * 150 * 1200 = $1,440,000
|
|
|
