Question 234844: A tourist agency can sell up to 1200 travel packages for a football game. The package includes 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 nonstop flight sells for $1200, and each package with a two-stop flight sells for $900. Assume that each plane will carry the maximum number of passengers. How do you suppose to graph this feasible region? What is the coordinates of the vertices of the feasible region?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! agency can sell up to 1200 travel packages for a football game.
The package includes 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 nonstop flight sells for $1200, and each package with a two-stop flight sells for $900.
Assume that each plane will carry the maximum number of passengers.How do you suppose to graph this feasible region?
What is the coordinates of the vertices of the feasible region?
:
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
:
Max revenue would be 8 full 150 pass planes at $1,440,000
Min revenue would be 10 full 100 pass planes at $900,000
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