Question

The Review Center offers a 3-day seminar on a variety of topics. In the seminar, each student is provided a different manual per day. The projected fee for the seminar is P1,000 per student. The cost for the conference room, instructor fee, assistants and promotion is P5,000. Review Center's printed manuals are at a cost of P200 per manual per day.

Answer the ff:
1. Develop a model for the total revenue.
R = ___x
2. Develop a model for the total cost to put on the seminar. Let x represent the number of students who enroll in the seminar.
Total Cost = ___ + ___*___*x = ___+___x
3. Develop a model for the total profit if x students enroll in the seminar.
Total Profit = Revenue – Cost = ___x - (___+___x) = ___x – ___
4. The review center has forecasted an enrollment of 100 students for the seminar. How much profit will be earned if their forecast is accurate? If 100 students were enrolled, then:
Profit = ___ * ___ – ___ = ___ – ___ = ___
5. What is the break-even point?
0 = ___x – ___ Therefore, X = ___

Answer 1

To calculate profits for a seminar, use the formula R = 1000x for total revenue. Total cost will be 5000 + 600x, and profit will be 400x - 5000. With 100 students enrolled, the profit is 35000, and the break-even point is 13 students.

Step-by-step explanation:

To calculate the total revenue for the seminar, the formula would be:

R = 1000x

Where x is the number of students enrolled, and each pays a fee of P1,000. For the total cost to put on the seminar, the cost includes a fixed fee and the cost of manuals which vary with the number of students:

Total Cost = Fixed Costs + (Cost per Manual per Day * Days * Number of Students)

Total Cost = 5000 + (200 * 3 * x) = 5000 + 600x

The profit model, with x representing the number of students, is:

Total Profit = Revenue - Total Cost

Total Profit = (1000x) - (5000 + 600x) = 1000x - 5000 - 600x = 400x - 5000

When 100 students are enrolled:

Profit = (400 * 100) - 5000 = 40000 - 5000 = 35000

The break-even point is where the total profit equals zero:

0 = 400x - 5000

X = 5000 / 400

X = 12.5

However, you cannot have a fraction of a student, so the break-even point would be at 13 students, as that is the smallest whole number greater than 12.5.