A certain travel agency offered a tourthat will cost each person P 1500.00 if not more than 150 persons will join,however the cost per person will be reduced by P 5.00 per person in excessof 150. what will be the maximum profit?
don't know about profit, but the revenue is price * quantity. So,
r(x) =
1500x if x <= 150
x(1500-5(x-150)) if x > 150
This is just a parabola with vertex at (225,253125), which is clearly greater than the flat rate for groups of less than 150.
To determine the maximum profit, we need to calculate the number of people who will join the tour at which the cost per person is the lowest.
Let's assume that x represents the number of people who will join the tour.
If not more than 150 persons join, the cost per person will be P 1500.00.
Therefore, the total cost will be 1500 * x if x <= 150.
If more than 150 persons join, the cost per person will be reduced by P 5.00 for each person in excess of 150.
Therefore, the total cost will be (150 * 1500) + (x - 150) * (1500 - 5).
To find the number of people that will minimize the cost per person, equate the two total cost equations:
1500 * x = (150 * 1500) + (x - 150) * (1500 - 5)
Simplifying the equation:
1500x = 225000 + (x - 150) * 1495
1500x = 225000 + 1495x - 1495 * 150
1500x = 225000 + 1495x - 224250
1500x - 1495x = 750
5x = 750
x = 750 / 5
x = 150
Therefore, the cost per person will be at its lowest if 150 people join the tour.
To calculate the maximum profit, subtract the total cost from the total revenue.
Total revenue = 150 * 1500 = 225000
Total cost = (150 * 1500) + (x - 150) * (1500 - 5) = (150 * 1500) + (150 - 150) * (1500 - 5) = 225000 + 0 = 225000
Maximum profit = Total revenue - Total cost = 225000 - 225000 = 0
Therefore, the maximum profit is 0.
To find the maximum profit, we need to determine the number of people that will result in the highest profit. Let's break down the problem step by step:
1. Determine the number of people that will result in the highest profit. To do this, we need to find the point where the cost per person equals the revenue per person. The cost per person is given as P 1500.00, and the revenue per person is calculated as P 1500.00 minus P 5.00 per person in excess of 150. We can represent this as an equation:
Revenue per person = Cost per person
P 1500.00 - P 5.00(x - 150) = P 1500.00
Simplifying the equation, we get:
P 1500.00 - 5x + 750 = P 1500.00
-5x + 750 = 0
-5x = -750
x = 150
Therefore, the maximum profit will be achieved when 150 people join the tour.
2. Calculate the maximum profit. The maximum profit is determined by multiplying the number of people (150) by the revenue per person at that point. The revenue per person can be calculated using the equation:
Revenue per person = P 1500.00 - P 5.00(x - 150)
Substituting x = 150:
Revenue per person = P 1500.00 - P 5.00(150 - 150)
Revenue per person = P 1500.00
Maximum profit = Revenue per person × Number of people
Maximum profit = P 1500.00 × 150
Maximum profit = P 225,000.00
Therefore, the maximum profit would be P 225,000.00.
Please note that this calculation assumes that there are at least 150 people joining the tour. If the number of people is fewer than 150, the cost per person would not be reduced.