A fruit seller sells oranges using a unique pricing strategy: if the ...
Understanding the Pricing Strategy
The fruit seller's pricing strategy is as follows:
- If the number of oranges bought is less than or equal to 100, the price per orange is fixed at Rs.10.
- For every additional orange above 100, a discount of Rs. (1/40) per orange is applied to the entire bunch.
Calculating Revenue for Different Values of 'n'
To find the value of 'n' that maximizes revenue, we need to calculate the revenue for different values of 'n' and identify the maximum revenue.
Let's calculate the revenue for 'n' oranges using the given pricing strategy:
If 'n' is less than or equal to 100:
- The price per orange is Rs.10.
- Therefore, the revenue for 'n' oranges is 10 * n.
If 'n' is greater than 100:
- The price per orange is Rs.10 minus the discount of (1/40) per orange.
- The total discount for the additional oranges is (n - 100) * (1/40).
- Therefore, the price per orange for the additional oranges is Rs.10 - (1/40).
- The revenue for 'n' oranges is (10 * 100) + [(n - 100) * (10 - (1/40))].
Finding the Maximum Revenue
To find the value of 'n' that maximizes revenue, we need to compare the revenue for different values of 'n' and identify the maximum revenue.
Let's calculate the revenue for different values of 'n' and find the maximum:
For n = 100:
- Revenue = 10 * 100 = Rs.1000.
For n = 101:
- Revenue = (10 * 100) + [(101 - 100) * (10 - (1/40))] = 1000 + (1 * 9.975) = Rs.1009.975.
For n = 102:
- Revenue = (10 * 100) + [(102 - 100) * (10 - (1/40))] = 1000 + (2 * 9.95) = Rs.1019.9.
Similarly, we can calculate the revenue for other values of 'n'.
Identifying the Maximum Revenue
By calculating the revenue for different values of 'n', we can observe that the revenue initially increases as 'n' increases. However, after a certain point, the revenue starts decreasing. We need to find the value of 'n' where the revenue is maximum.
Based on the calculations, we can observe that the maximum revenue is obtained when 'n' is 250, which is Rs.2475.
Therefore, the value of 'n' that maximizes revenue is 250.