Advancing Quantitative Reasoning Skills- Emphasis in Assessment

Advancing Quantitative Reasoning Skills- Emphasis in Assessment

Problem #1

Part 1a

Given the general equation i.e., y = mx + c Where:

y = number of workers

x = number of years

c = number of workers in the initial year

m = the rate of change

Then:

14.7 = m (18) + 16.3

18m = 14.7-16.3

m = -1.6/18

m = 0.089

Therefore, the equation will be y = -0.089x + 16.3

Part 1b

In 2050, x = 50

Thus, y = -0.089x + 16.3

y = -4.4 + 16.3

y = 11.9 million

Thus, in 2050, there will be 11.9 million unionized workers.

Part 1c

Yes, given that other variables stay the same, the figure in 1b is reasonable. Nonetheless, a variety of factors may influence an employee’s decision to form a union. For instance, the government may pass new legislation mandating labor union membership for workers in particular sectors of the economy. Notably, this would result in a sharp rise in the number of workers belonging to labor unions. Additionally, more companies might implement rules that prevent workers from becoming members of labor unions, which would quicken the rate at which union membership is dropping. However, as more workers choose not to join unions, the number of unionized workers will continue to fall, all other things being equal. Other factors that can alter the future numbers of work unions include technological advancements and international trade dynamics (Haipeter, 2020). Essentially, as technology advances increase, the need for labor unions and their influence may be reduced. As a result, the number of workers may not grow in line with the equation generated.

Problem #2

Part 2a

y = mx + 529000

Given that y = 498,780

x = 28

Then,

498780 = m (28) + 529000

-30220 = 28m

m = -30220/28

m = -1079.29

Thus, the equation will be y = -1079.29x+529,000

Part 2b

Given the equation y = -1079.29x + 529,000

Given y = 400,000

Then we find x, i.e., 400,000 = -1079.29x + 529000 400,000-529000 = -1079.29x

x = 129,000/1079.29

x =119.5

Therefore, it will take 120 years from the year 1990 until the number of employees in the air transportation industry reaches 400,000, which results in the year 2110.

Part 2c

The figure in 2b is realistic. Automation plays a major role in this industry’s employee decline. The number of employees will not change if the rate of automation stays the same. Nevertheless, the rate of decline will be higher than that predicted by the above equation if the industry’s automation pace quickens and more jobs become obsolete. For instance, while some airlines have moved their ticketing systems online, others are thinking about deploying automated cashiers and ticketing systems. The workforce in this sector is still getting smaller because of these actions.

Problem #3

Part 3b

Given the general equation that y = mx +c in 1990

y = 1.1 million

x = 0

Therefore, c =1.1 million

In 2018, given y = 1.5 million, x =28 Then

1.5 = 28m + 1.1

1.5 – 1.1 = 28m

m = 0.4/28

m = 0.014

Thus, the equation is y = 0.014x + 1.1

Part 3b

Given y = 2.5 and the equation above remains valid,

Then 2.5 = 0.014x + 1.1

1.4 = 0.014x

x =1.4/0.014 x = 100

Thus, there will be 2.5 million employees after 100 years from 1990, which is in the year 2090.

Part 3c

The figure in above 3b is realistic. Over the past few years, the trucking industry has seen an increase in the number of employees. As predicted in above b, the number would keep rising if all other variables remained unchanged. However, the number of workers in this sector would decline due to things like the introduction of automated trucks. In addition, since more cargo owners would choose the less expensive railway, the trucking industry may be greatly impacted by the expansion of the railway network. Furthermore, the future numbers in the trucking industry may change based on the increased level of electrical vehicles. Notably, the increase reduces expenses on fuel which can attract more people into the sector (Lookman et al., 2023). As a result, the number of future employees in the sector may increase.

References

Haipeter, T. (2020). Digitalization, unions, and participation: The German case of ‘industry 4.0’. Industrial Relations Journal, 51(3), 242-260.

Lookman, K., Pujawan, N., & Nadlifatin, R. (2023). Innovative capabilities and competitive advantage in the era of Industry 4.0: A study of the trucking industry. Research in Transportation Business & Management, 47, 100947.

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In this assignment, your quantitative reasoning skills will be assessed. The Quantitative Reasoning rubric will be useful for this purpose. In MGT511 quantitative reasoning skills were assessed at the “introduced” level. In HRM520 they were assessed at the “reinforced” level. Finally, in this course, your skills will be assessed at the “emphasized” level.

The math that we learned in high school and perhaps relearned in college has applications in nearly all fields including human resource management. In this case assignment we will look at something as simple as straight lines, as in linear equations.

Straight lines play an important role in a wide variety of applications, in many fields including business.

An equation with two variables is a linear equation. Many relationships are linear or almost linear so they can be approximated by linear equations.

If you need a refresher on solving equations, watch the Khan Academy, level 2 video retrieved from https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-2

Example:

The following linear equation is useful to make a future projection:

In 1970, there were 37,000 shopping malls in the United States.

Even with the growth of online shopping, in 2017 there were 116,000 shopping malls.

If this growth continues, how many shopping malls will there be in 2030?

Let’s use two variables:

y = number of shopping centers

x = number of years after 1970

So, to put this in an equation:

So, the linear equation is y = 1681x + 37,000

Now, assuming that this equation remains valid in the future, we can predict how many shopping malls there will be in 2030:

There are 60 years between 1970 and 2030.

y = 1681(60) + 37,000

y = 100,860 + 37,000 or 137,860 shopping malls in 2030.

This example probably reminds you that there might be other factors going on that will not make this equation valid in the future. But, for our purposes, it shows if all things stay the same, we can make future predictions.

There are many different examples of ways linear equations are used in real life—for example, the distance traveled by a bus compared with the distance traveled by a bicycle. Which one will get to work on time? Or, production rates—will employees who are slow producers make as many products over time as employees who are only speedy during the first part of the shift? This type of linear application can also be applied, of course, to pricing, dimensions, and mixing raw products. For example, if we have two semi-trucks of products moving toward each other at different speeds to reach the same point, which one will reach the dock sooner? Another example is estimating how much a box of 60 safety glasses is on sale for $120 and marked down by 35 percent cost before the sale.

Yet another example of a real-life linear equation is estimating the dimensions of office shelving whose width needs to be four times its height, given that the wood available for use is 72 feet. Or, estimating how much a company pays a vendor for raw material that was priced yesterday for $800, but today has been marked up 25 percent.

Case Assignment
Now it is your turn. For the Module 4 Case Assignment, solve the following three problems, completing a, b, and c for each problem. In “b” for each, explain step by step how you arrived at the answer. In “c” for each, conduct research to arrive at a strong (informative) paragraph, being sure to cite sources.

Problem #1: According to the U. S. Bureau of Labor Statistics, there were about 16.3 million union workers in 2000 and 14.7 million union workers in 2018.

If the change in the number of union workers is considered to be linear, write an equation expressing the number y of union workers in terms of the number x of years since 2000.
Assuming that the equation in part “a” remains accurate, use it to predict the number of union workers in 2050.
Is the number that you came up with in 1b realistic? Why or why not? What can interfere with the future number of union workers that the equation does not account for?
Problem #2: According to the U.S. Bureau of Labor Statistics, in 1990, 529,000 people worked in the air transportation industry. In 2018, the number was 498,780.

Find a linear equation giving the number of employees in the air transportation industry in terms of x, the number of years since 1990.
Assuming the equation remains valid in the future, in what year will there be 400,000 employees in the air transportation industry?
Is the number you came up with in 2b realistic? Why or why not? What can interfere with the future number of employees working in the air transportation industry that the equation does not account for?
Problem #3: The U.S. Bureau of Labor Statistics estimated that in 1990, 1.1 million people worked in the truck transportation industry. In 2018, the number was 1.5 million.