Let:
e = Number of economy seats sold
d = Number of deluxe seats sold
There are some restrictions on the tour:
* At least 1 economy seat must be sold, that is:
e ≥ 1
* At least 6 deluxe seats must be sold, thus:
d ≥ 6
* The maximum number of passengers is 30, thus:
e + d ≤ 30
The profit is $40 for each economy seat sold and $35 for each deluxe seat sold:
P = 40e + 35d
This is the function to maximize subject to the restrictions above. We'll use the graph method.
It requires graphing the lines e = 1, d = 6, and e + d = 30 on the same grid and find the feasible region.
The feasible region is a triangle with vertices at (1, 6), (24, 6), and (1, 29).
Now we test the vertices in the function to maximize.
For (1, 6):
P = 40(1) + 35(6)
P = 250.
For (24, 6):
P = 40(24) + 35(6)
P = 1170
For (1, 29):
P = 40(1) + 35(29)
P = 1055
Thus, the maximum profit ($1120) is done when 24 economy seats and 6 deluxe seats are sold.
