To make a contractual obligation, a company must make 90 units of a pr

Given Information:
1. The company must produce 90 units in 7 days.
2. Each employee produces 2 units per day.
3. In the first 5 days, 30 units are completed. Therefore, 60 units remain for the last 2 days.
4. During the last 2 days, additional workers are hired, each producing \(r\) units per day.
5. Condition: \(a < r\).

Step 1: Employees Working for the First 5 Days
Let’s assume the company starts with \(a\) workers. In 5 days:

\(\text{Units produced} = 5 \cdot 2 \cdot a = 10a\)
This means:
\(10a = 30 \implies a = 3\)

So, initially, there are 3 workers.

Step 2: Units Remaining in the Last 2 Days
The remaining units to be produced are:
90 - 30 = 60

Step 3: Total Work Done in the Last 2 Days
For the last 2 days, the initial \(a = 3\) workers continue to work, and additional workers are hired. Total work done in 2 days is:
\(\text{Total work} = (3 + \text{additional workers}) \cdot r \cdot 2\)

If \(b\) is the number of additional workers, then:
\(2 \cdot (3r + br) = 60\)

Solving for values consistent with \(a < r\), we find that:
\(a = 4 \quad \text{and} \quad r = 6\)