A salesman has to choose between two schemes of remuneration.The first scheme has a fixed salary of rs 3700 and a commission of 2% on sales above rs 50000. The second scheme has no salary but offer commission only. The commission starting from 3% of sales for the first rs 50000 or part there of increase at the rate of 1 percentage point for every increase of rs 50000 or part there of sales upto a maximum of 20% of sales. what is the minimum value of sales above which he can prefer the second scheme ?
Please explain easy way
To determine the minimum value of sales above which the salesman would prefer the second scheme, we need to compare the total earnings from both schemes.
Let's analyze each scheme separately:
First Scheme:
Fixed Salary: Rs 3700
Commission: 2% on sales above Rs 50000
Second Scheme:
No Salary, only Commission
Commission rates: Starting from 3% for the first Rs 50000 or part thereof, increasing by 1 percentage point for every increase of Rs 50000 or part thereof, up to a maximum of 20%.
To find the minimum value of sales where the second scheme becomes preferable, we need to find the point at which the earnings from the second scheme exceed the earnings from the first scheme.
Let's break it down step by step:
Step 1:
In the first scheme, the salesman earns a fixed salary of Rs 3700, regardless of the sales.
Step 2:
In the second scheme, the salesman earns commissions based on sales. The commission rates increase as follows:
- 3% for the first Rs 50000 or part thereof
- Increase by 1% for every increase of Rs 50000 or part thereof
- Up to a maximum of 20% of sales
Step 3:
To calculate the earnings using the second scheme, we need to determine the sales threshold where the commission percentage reaches 20%. This means that the commission percentage will increase by 1 percentage point for every Rs 50000 increase in sales until reaching 20%.
Step 4:
Let's determine the sales threshold for the 20% commission:
The increase in commission rate is 1% for every Rs 50000 increase in sales.
To reach 20%, there would need to be 19 additional increases of 1% (since the initial rate is 3%).
Hence, the sales threshold for the 20% commission is Rs 50000 + (19 * Rs 50000) = Rs 1000000.
Step 5:
Now, let's compare the earnings of both schemes. For simplicity, let's assume the sales exceed the sales threshold for the 20% commission (i.e., Rs 1000000).
First Scheme:
Fixed Salary = Rs 3700
Commission = 2% of sales above Rs 50000
For sales of Rs 1000000:
Commission = 2% * (Rs 1000000 - Rs 50000) = Rs 19000
Total Earnings = Fixed Salary + Commission
= Rs 3700 + Rs 19000
= Rs 22700
Second Scheme:
No Salary, Only Commission
For sales of Rs 1000000:
Commission = 20% of sales = 20% * Rs 1000000 = Rs 200000
Total Earnings = Commission
= Rs 200000
Step 6:
By comparing the total earnings of both schemes, we can see that the second scheme (commission only) is preferable if the sales exceed the sales threshold for the 20% commission. In this case, the minimum value of sales above which the salesman would prefer the second scheme is Rs 1000000.
Therefore, if the sales exceed Rs 1000000, the salesman would choose the second scheme for higher earnings.
To determine the minimum value of sales above which the salesman will prefer the second scheme, we need to compare the total earnings of both schemes.
Let's break it down step by step:
First Scheme:
- Fixed salary = Rs 3700
- Commission rate = 2% on sales above Rs 50000
Second Scheme:
- No fixed salary
- Commission rate starting from 3% for the first Rs 50000 or part thereof
- Commission rate increases by 1 percentage point for every increase of Rs 50000 or part thereof, up to a maximum of 20% of sales
To find the minimum value of sales where the second scheme becomes more advantageous:
1. Calculate the commission earnings for both schemes based on the sales:
For the First Scheme:
- Commission earnings = 2% of (sales above Rs 50000)
For the Second Scheme:
- Commission earnings = (Commission rate) * (sales)
2. Calculate the total earnings for both schemes:
For the First Scheme:
- Total earnings = Fixed salary + Commission earnings
For the Second Scheme:
- Total earnings = Commission earnings
3. Set up and solve the equation to find the minimum value of sales:
(Total earnings for the Second Scheme) > (Total earnings for the First Scheme)
So, the formula would be:
(Commission earnings for the Second Scheme) > (Fixed salary + Commission earnings for the First Scheme)
Plug in the values:
(Commission rate * sales) > (Fixed salary + Commission rate * (sales above Rs 50000))
At this point, we need to find the value of sales that satisfies this equation. You can start with a value for sales and calculate the total earnings for both schemes. If the total earnings for the second scheme become higher at a certain sales value, then that becomes the minimum value.
Continue this trial and error process until you find the minimum value of sales for which the second scheme becomes more advantageous.