By how much vendor B's sales have to be increased in order to justify the doubling of the number of employees at the same rate of pay, if B's desired operating income is 350?

Understanding the Problem

The problem states that Vendor B wants to double its employee count at the same rate of pay. This implies a doubling of labor costs. The goal is to determine the increase in sales required to offset this increased cost and still achieve a desired operating income of 350. We need to make some assumptions to proceed, as the initial sales and employee count are not provided. Let's denote:

• S = Current Sales of Vendor B
• E = Current Number of Employees
• P = Pay per Employee
• OI = Current Operating Income

Therefore, Current Labor Cost = E * P. We are given that the desired operating income after doubling employees is 350.

Setting up the Equation

Let's assume the current operating income is OI. The current operating income can be expressed as:

OI = S - (E * P) - Other Costs

Where 'Other Costs' represent all expenses besides labor. We will assume 'Other Costs' remain constant. When the number of employees is doubled (2E), the new labor cost becomes 2 * (E * P). Let 'S_new' be the new sales required to achieve the desired operating income of 350.

350 = S_new - (2E * P) - Other Costs

We want to find the increase in sales, which is (S_new - S). Subtracting the first equation from the second equation, we get:

350 - OI = (S_new - S) - (2E * P - E * P)

350 - OI = (S_new - S) - (E * P)

Therefore, (S_new - S) = 350 - OI + (E * P)

This equation tells us that the required increase in sales depends on the current operating income (OI), the current labor cost (E * P), and the desired operating income (350). Since we don't have values for OI, E, and P, we need to make an assumption. Let's assume the current operating income (OI) is 0. This means the business is currently breaking even.

Then, (S_new - S) = 350 + (E * P)

This means the sales have to increase by 350 plus the current labor cost to justify doubling the employees.

Illustrative Example

Let's assume Vendor B currently has 10 employees (E = 10) and each employee is paid 10,000 per year (P = 10,000). Therefore, the current labor cost is 10 * 10,000 = 100,000. If we assume OI = 0, then the required increase in sales is:

S_new - S = 350 + 100,000 = 100,350

This means Vendor B's sales need to increase by 100,350 to justify doubling the number of employees.

Considering Different Scenarios

If the current operating income is not zero, the required sales increase will be different. For example, if the current operating income is 50,000, then the required sales increase would be:

S_new - S = 350 - 50,000 + 100,000 = 50,350

In this case, the sales increase required is significantly lower because the business is already profitable.

Limitations

This analysis assumes that 'Other Costs' remain constant. In reality, increased sales volume might lead to higher costs for materials, marketing, or distribution. A more comprehensive analysis would need to consider these factors.