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 ?

Question

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 ?

Answer 1

for x in sales, we have

scheme 1:
3700 + .02(x-50000)
that works out to
3700 for x <= 50000
3700 + .02x for 50000 < x <= 100000
4700 + .02x for 100000 < x <= 150000

scheme 2:
.03x for x <= 50000
1500 + .04x for 50000 < x <= 100000
3500 + .05x for 100000 < x <= 150000

I think you can figure out now how to get the place where they are equal.

Answer 2

To find the minimum value of sales above which the salesman would prefer the second scheme, we need to compare the total earnings of both schemes.

Let's start by calculating the earnings under the first scheme:
- Fixed salary: Rs 3700
- Commission: 2% of sales above Rs 50000

Now, let's calculate the earnings under the second scheme:
- Commission: Varies with the level of sales

To solve this, we'll calculate the total earnings under both schemes for different values of sales and find the point at which the earnings from the second scheme becomes greater than the fixed salary plus commission from the first scheme.

Let's calculate the earnings for different amounts of sales under the second scheme:

For sales up to Rs 50000, the commission is 3% of sales.
Earnings = 0.03 * sales

For sales between Rs 50000 and Rs 100000, the commission increases by 1% for every increase of Rs 50000 or part thereof.
Earnings = 0.03 * 50000 + 0.04 * (sales - 50000)

For sales between Rs 100000 and Rs 150000, the commission continues to increase by 1% for every increase of Rs 50000 or part thereof.
Earnings = 0.03 * 50000 + 0.04 * 50000 + 0.05 * (sales - 100000)

...

Continue this pattern until the commission reaches a maximum of 20% for sales above Rs 500000.

Compare the total earnings from the second scheme with the total earnings from the first scheme for each sales amount.

The minimum value of sales above which the salesman would prefer the second scheme is the point at which the earnings from the second scheme become greater than the total earnings from the first scheme.

So, by calculating the total earnings for different sales amounts for both schemes, you can determine the minimum value of sales above which the salesman would prefer the second scheme.