Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seat must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour?
for x economy and y deluxe seats, you want to
maximize p = 40x + 35y
subject to the constraints
x >= 1
y >= 6
x+y <= 30
So proceed as usual, drawing the region and evaluating p at the vertices.
To find the maximum profit from one tour, we need to determine the number of economy seats and deluxe seats that should be sold.
Since at least 1 economy seat must be sold, we can start by assuming that 1 economy seat is sold. Now, we need to find the maximum number of deluxe seats that can be sold.
To complete the tour, at least 6 deluxe seats must be sold. However, the maximum number of passengers allowed on each boat is 30. So, if we assume that 6 deluxe seats are sold, the remaining number of seats available for passengers would be 30 - 6 = 24.
Now, let's calculate the maximum profit from the economy seats and deluxe seats:
Profit from selling 1 economy seat = $40
Profit from selling 6 deluxe seats = $35 * 6 = $210
Since the remaining number of seats available is 24, we can assume that all of them are deluxe seats. So, the profit from selling the remaining deluxe seats would be $35 * 24 = $840.
Now, let's calculate the maximum profit from one tour:
Maximum profit = Profit from economy seats + Profit from deluxe seats
= $40 + $210 + $840 = $1090
Therefore, the maximum profit from one tour is $1090.