Tanner Park is a small amusement park that provides a variety of rides and outdoor activities for children and teens. In a typical summer season, the number of adult and children’s tickets sold are 20,000 and 10,000, respectively. Adult ticket prices are $18 and the children’s price is $10. Revenue from food and beverage concessions is estimated to be $60,000, and souvenir revenue is expected to be $25,000. Variable costs per person (adult or child) are $3, and fixed costs amount to $150,000.
a. Determine the profitability of this business.
b. Now change the model based on the following information. In a typical summer season, the number of adult tickets sold has a normal distribution with a mean of 20,000 and a standard deviation of 2,000. The number of children’s tickets sold has a normal distribution with a mean of 10,000 and a standard deviation of 1,000. Adult ticket prices are $18 and the children’s price is $10.Revenue from food and beverage concessions is estimated to be between $50,000 and $100,000, with a most likely value of $60,000. Likewise, souvenir revenue has a minimum of $20,000, most likely value of $25,000, and a maximum value of $30,000. Variable costs per person are $3, and fixed costs amount to $150,000. Determine the profitability of this business. What is the probability that the park will incur a loss in any given season?