Island Water Sports is a business that provides rental equipment and instruction for a variety of water sports in a resort town. On one morning, a decision must be made of how many Wildlife Raft Trips and how many Group Sailing Lessons should be scheduled. Each Wildlife Raft Trip requires one captain and one crew person and can accommodate six passengers. The revenue per raft trip is $120. Ten rafts are available, and at least 30 people are on the list for reservations this morning.
Each Group Sailing Lesson requires one captain and two crew people for instruction. Two boats are needed for each group. Four students form each group. There are 12 sailboats available, and at least 20 people are on the list for sailing instruction this morning. The revenue per group sailing lesson is $160. The company has 12 captains and 18 crew available this morning. The company would like to maximize the number of customers served while generating at least $1800 in revenue and honoring all reservations.

To determine how many Wildlife Raft Trips and Group Sailing Lessons should be scheduled to maximize the number of customers served while generating at least $1800 in revenue and honoring all reservations, we can use a linear programming model.

Let:

r = number of Wildlife Raft Trips

s = number of Group Sailing Lessons

Let the total revenue be R = 120r + 160s

The total number of customers served will be 6r + 2s

The constraints are:

r >= 30

s >= 20

r >= s

r <= 10

s <= 9