By December 2014, your organization had an establishment of 500 employees when it decided to expand its operations because of growth of market products demand. The decision was to increase the labor strength progressively by 5 percent per annual over the two year period while accommodating an annual wastage of 8 percent,

A) project labor authorization for January 2017 and
B). What is the estimated budget for the recruitment exercise if the estimated cost of recruiting one employee during the period would be k1500.

To find the projected labor authorization for January 2017, we need to calculate the number of employees your organization plans to have by that time.

Let's break down the steps:

Step 1: Calculate the labor strength for December 2014.
The initial labor strength is 500 employees.

Step 2: Calculate the labor strength for each subsequent year.
To increase the labor strength by 5% annually, we need to determine the number of employees to add each year. To do this, we multiply the current labor strength by 0.05 (5%) to get the number of employees to add. Then we subtract the annual wastage of 8% to account for employees leaving the company.

For Year 1:
Number of employees to add = 500 * 0.05 = 25
Annual wastage = 500 * 0.08 = 40
Labor strength for Year 1 = 500 + 25 - 40 = 485 employees

For Year 2:
Number of employees to add = 485 * 0.05 = 24.25 (rounding to the nearest whole number)
Annual wastage = 485 * 0.08 = 38.8 (rounding to the nearest whole number)
Labor strength for Year 2 = 485 + 24 - 38 = 471 employees

Step 3: Project labor strength for January 2017.
To find the projected labor strength for January 2017, we need to add the labor strength for December 2014 to the labor strength from Year 1 and Year 2.

Projected labor strength for January 2017 = 500 + 485 + 471 = 1456 employees

A) Project labor authorization for January 2017: The projected labor authorization for January 2017 is 1456 employees.

B) To calculate the estimated budget for the recruitment exercise, we multiply the projected labor authorization (1456) by the estimated cost of recruiting one employee during the period (k1500).

Estimated budget = 1456 * k1500 = k2,184,000