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 ?
To determine the minimum value of sales above which the salesman would prefer the second scheme, we need to compare the earnings under both schemes and find when the second scheme becomes more favorable.
Let's calculate the earnings under the first scheme:
Fixed salary = Rs 3,700
Commission = 2% of sales above Rs 50,000
Now let's calculate the earnings under the second scheme:
Commission rates range from 3% to a maximum of 20% based on the sales amount.
To find the minimum sales value above which the second scheme is preferred, we need to compare the earnings under both schemes and find the point where the second scheme surpasses the first scheme.
Let's solve this step by step:
1. Calculate the earnings under the first scheme:
- Fixed salary = Rs 3,700
- Commission = 2% of sales above Rs 50,000
Let's assume the sales value as 'x' for further calculations.
Therefore, earnings under the first scheme = Rs 3,700 + 2% * (x - Rs 50,000)
2. Calculate the earnings under the second scheme:
We need to consider the commission rates based on the sales amount.
- For the first Rs 50,000 or part thereof, the commission is 3%.
- For every increase of Rs 50,000 or part thereof, the commission increases by 1 percentage point, up to a maximum of 20%.
Let's assume the sales value as 'y' for further calculations.
Therefore, the commission for the second scheme can be determined as follows:
- If y <= Rs 50,000, commission = 3% of y
- If Rs 50,000 < y <= Rs 100,000, commission = 3% of Rs 50,000 + (1% * (y - Rs 50,000))
- If Rs 100,000 < y <= Rs 150,000, commission = 3% of Rs 50,000 + 1% of Rs 50,000 + (1% * (y - Rs 100,000))
- Following the same pattern, continue the calculation until the commission reaches a maximum of 20%.
3. Equate the earnings under both schemes and solve for the sales value 'z':
Rs 3,700 + 2% * (z - Rs 50,000) = commission under the second scheme
Solve the equation to find the value of 'z,' which represents the minimum sales value above which the second scheme is preferred.
Calculating the exact minimum value requires further calculations, but this process will guide you to find the answer step by step.