Question 164697This question is from textbook Algebra 2
: 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 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 inequalities to represent the constraints.
b. Graph the feasible region.
c. Write the objective function that maximizes the revenue for the tourist agency.
d. Find the maximum revenue.
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I need help with parts a and c.
This question is from textbook Algebra 2
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 package includes airfare, weekend accommodations, and the choice of two types of flights: a nonstop flight or a two-step 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, each package with a two stop flight sells for $900. Assume that each plane will carry the maximum amount 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
:
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
------------------
total rev = $1,260,000
:
x,y
8,0
8*150*1200 = 1440000
0*100*900 = 0
---------------------
total rev = $1,440,000
:
It looks like you load up 8 nonstop planes at $1200 ea, for max revenue
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