Question 495560
a tourist agency can sell up to 1200 packages for a football game. the package includes airfare, weekend accomodations, 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. assume that each plane will carry the maximum number of passengers. 
:
A. Write a system of linear equalities to represent the constraints.
Let x = no. of non-stop airplanes
Let y = no. of 2-stop airplanes
:
total passenger constraint
150x + 100y =< 1200
:
Total Airplanes constraint
x + y =< 10
:
B.Graph the feasible region.
Arrange the above equations for graphing
150x + 100y = 1200
100y = 1200 - 150x
y = 12 - 1.5x; purple
and
x + y = 10
y = 10 - x; green
:
{{{ graph( 300, 200, -4, 10, -4, 15, 12-1.5x, 10-x) }}}
Feasibility region is all positive values at or below either line, which ever is lowest.
: 
C.Write an objective function that maximizes the revenue for the tourist agency, and find the maximum revenue for the given constraints.
:
x,y 
0,10: revenue 
0*150*1200=0,
10*100*900 = 900,000 
----------------
total $900,000
:
x,y
4,6
4*150*1200 =720000
6*100*900 = 540000
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total rev = $1,260,000
:
x,y
8,0
8*150,1200 = 1440000
0*100,900 = 0
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total rev = $1,440,000
:
It looks like you load up 8 nonstop planes at $1200 ea, for max revenue