3. Hibiscus Sdn. Bhd, a tourist company based at Johor Bharu is offering bus travelling
to three different locations: Phuket and Krabi in Thailand and also Sungai Petani in
Kedah. The routes and distances are as follows:
Johor Bharu - Kuala Lumpur – Kota Bharu – Pattani – Songkla – Phuket : 1500 km
Johor Bharu – Kuala Lumpur – Ipoh – Songkla – Krabi : 1140 km
Johor Bharu – Kuala Lumpur – Ipoh – Sungai Petani : 720 km
The average fare per trip is not more than RM2000. As for the company travelling
cost, it is expected that travelling to Sungai Petani will take about 10% from the bus
fare, 12% for Phuket and 14% for Krabi.
The company wants to ensure that the overall average cost is not more than 10%
of earned bus fare. The company conclude that it could sell about 1900 tickets to
travel to Sungai Petani, 1000 tickets heading to Krabi and 700 tickets to Phuket.
a. By considering all stated conditions and assuming all tickets are sold, in
maximizing its total revenue, determine how much should the company charge
per ticket.
b. In maintaining its competitive advantages, the company can only charge not
more than RM4000 per ticket to Sungai Petani and Krabi. Assuming all other
constraints will remain the same, calculate the ticket price and the maximum
revenue.
To determine the ticket price and maximum revenue, we need to calculate the revenue generated from each destination and then find the maximum revenue by adjusting the ticket price accordingly.
a. To maximize total revenue:
- Let x be the ticket price.
- Revenue from Sungai Petani: 1900 * x
- Revenue from Krabi: 1000 * x
- Revenue from Phuket: 700 * x
- Total revenue = Revenue from Sungai Petani + Revenue from Krabi + Revenue from Phuket
The total revenue should not exceed 10% of the earned bus fare, which is 0.1 * (1900 * x + 1000 * x + 700 * x).
We also know that the average fare per trip is not more than RM2000. So, we can set the equation:
0.1 * (1900 * x + 1000 * x + 700 * x) ≤ 2000
Solving the equation:
0.1 * (3600x) ≤ 2000
360x ≤ 2000
x ≤ 2000/360
x ≤ 5.56
Therefore, the company should charge not more than RM5.56 per ticket to maximize its total revenue.
b. Considering the maximum ticket price constraint:
- Let x be the ticket price again.
- Revenue from Sungai Petani: 1900 * x
- Revenue from Krabi: 1000 * x
- Revenue from Phuket: 700 * x
- Total revenue = Revenue from Sungai Petani + Revenue from Krabi + Revenue from Phuket
Since the ticket price for Sungai Petani and Krabi cannot exceed RM4000, we set the equation:
Ticket price (x) ≤ RM4000
Therefore, the maximum ticket price that the company can charge is RM4000.
To calculate the maximum revenue, we plug in the maximum ticket price into the revenue formula:
Total revenue = (1900 * 4000) + (1000 * 4000) + (700 * 4000)
Total revenue = 7,600,000
Hence, with a maximum ticket price of RM4000, the maximum revenue the company can earn is RM7,600,000.