Question

I NEED HELP ASAP,THANKS! :)

Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats 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? Show work.

Answer 1

$1170

Explanation:

Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...

• x ≥ 1
• y ≥ 6
• x +y ≤ 30

And the objective function we want to maximize is ...

p = 40x +35y

__

I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.

Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...

24 economy seats and 6 deluxe seats

The corresponding profit will be ...

24(40) +6(35) = 1170

The maximum profit from one tour is $1170.