Question

Apparently all the computer records were lost during the transition. All I have are a few notes scratched on a piece of paper to guide me. We have three pay levels. Level 1 employees begin at $15,000. The notes say that in the third year the salary should rise to $19,000. Level 2 employees start at $30,000 and according to the notes their salary should rise to $36,000 in year 3. Finally, Level 3 employees start at $50,000 and the notes say that they should be making $58,000 by the end of year 3. The only other piece of information I have is that the growth of salary over time is supposed to follow a linear growth pattern - whatever that means. The notes also say that once a Level 1 employee has worked long enough to reach a salary of $30,000 he or she should either be promoted to Level 2 or fired. The same applies to Level 2 employees when they reach $50,000 in salary. Can you help me out

Answer 1

Answer:

hello your question lacks some parts so i will include the part lacking

  I need first to know what exactly is the rate of increase for each level of employee over time.  I would also like a mathematical model that will allow me to input the number of years the employee has been working for us and give back their current salary. Finally, I would like to know after how many years of working for us a Level 1 employee should expect to be promoted to Level 2 and after how many years of working for us can a Level 2 employee be promoted to a Level 3.  With this information I can begin to bring some order back to Human Resources.  Please fully explain how you figured all this out. If my boss asks where these numbers are coming from, I want to explain to him what you did.  

Answers:  Rate of increase for level 1 = $2000  annually

                 Rate of increase for level 2 = $3000 annually

                 Rate of increase for level 3 = $2666.67 annually

The mathematical model is  Y = cx + d

It will take a level 1 employee 7.5 years to attain promotion to level 2

It will take a level 2 employee approximately 7 years to attain promotion to level 3

Explanation:

Level 1 employees will have their salary raised from $15000 to $19000 at the beginning of the third year therefore the rate of increase of their salary would be = change in salary/time duration

                = $19000 - $15000 / 2 years

                = $4000 / 2 = $2000 increase per year

Level 2 employees will have their salary increase from $30000 to $36000 at the beginning of the third year hence the rate of increase of their salary would be = change in salary/time duration

                                   = $36000 - $30000 / 2 years

                                   = $6000 / 2 = $3000 increase per year

Level 3 employees will have their salary increase from $50000 to $58000 by the end of the third year hence the rate of increase of their salary would be = change in salary/time duration

    = $58000 - $50000 / 3

    = $8000 / 3 = $2666.67

The mathematical model to be used can be a simple mathematical formula that shows the relationship between the rate of increase of the salary, current salary, starting salary and the number of years worked

such formula can be expressed as Y = cx + d

x = number of years

c = rate of increase in salary

d = starting salary

y = current salary

From the question when a level 1 employee reaches a current salary of $30000 the employee should be promoted or fired hence to find the number of years before a level 1 employee achieves this. use the formula

Y = cx + d

$30000 = $2000 x + $15000

$30000 - $15000 = $2000 x

hence x ( number of years ) = $15000 / $2000 = 7.5 years

when a level 2 employee reaches a current salary of $50000 the employee should as well be promoted or fired hence to find the number of years before the employee at level 2 attains this we use the formula

Y = cx + d

$50000 = $3000 x + $30000

$50000 - $30000 = $3000 x

hence x ( number of years required from employee at level 2 to attain this ) = $20000 / $3000 = 6.7 years approximately 7 years

Answer 2

Answer: 1) 2000/yr, 3000/yr, 4000/yr

2) y = ax + b

3) 7.5yrs, 6.7yrs

Explanation:

 We need first to know what exactly is the rate of increase for each level of employee over time. Also a mathematical model that will allow to input the number of years the employee has been working and give back their current salary. Finally, the years of working Level 1 employee should expect to be promoted to Level 2 and after how many years of working Level 2 employee be promoted to a Level 3.  

Solution:

Rate of increase( slope) = increase/number of years.

Level 1

(19000 - 15000)/2 =4000/2 = 2000/year

Level 2

(36000 - 30000)/2 = 6000/2 = 3000/year

Level 3

(58000 - 50000)/2 = 8000/2 =4000/year

Mathematical model: y = ax + b

Where y = current salary

X = number of years

a = slope

b = starting salary

Number of years of promotion:

Level 1

30000 = 2000x + 15000

X = 7.5yrs

Level 2

50000 = 3000X + 30000

X = 6.7yrs