Vol 66, No. 7 - International Technology and Engineering Educators ...

estimates and decisions about tool purchases, workstation
design, and production flow.
D ay 3—Estimating Costs U sing A pplied A lgebra
An overview of the final day’s activities included a review
of manufacturing engineering roles and an examination
of how algebra skills are used to inform cost-related
decisions in manufacturing engineering. The review
consisted of questions that guided group discussion,
including:
1. What are the primary goals of a manufacturing engineer?
How do the responsibilities and skills of a methods
engineer, planning specialist, and time analyst differ?
2. What strategies do engineers use to ensure the
consistent and efficient manufacture of products?
Discuss tooling (fixtures and templates) and a methods
instruction sheet.
3. What algebra concepts and procedures do time analysts
employ? Discuss symbolic representation, variables,
and equations.
After ample time for discussion, students were reminded
that a primary goal of a manufacturing company is to sell
their manufactured products to make a profit. Typically,
the finance department of a company oversees the balance
of costs (e.g., materials, energy, labor, and equipment),
market price, and profits. However, estimating, reducing,
and controlling the costs of manufacturing a product lie
within the purview of manufacturing engineers. So, in
addition to the technical aspects of processing materials,
engineers must possess the skill to apply many mathematical
processes (e.g., capacity or break-even analysis) to inform
cost decisions. For instance, the decisions engineers make
about which equipment will be purchased for a workstation
directly impact the cost of the labor required to perform the
operation. Carefully planning, estimating, and controlling
manufacturing costs requires engineers to employ a variety
of algebra concepts and skills, including using symbolic
expressions to represent costs, organizing costs into
matrices, and solving equations to estimate costs.
At this point, workstation groups were offered the following
challenge: Conduct a cost analysis of three tools that could
be selected for a manufacturing operation. Specifically,
this analysis should determine at what point (i.e., number
of cycles) the cost of labor is greater than the cost of the
tool, then offer recommendations about the purchase of
equipment or the process of conducting a cost analysis.
Students were reminded to assume the role of cost
estimators. Specifically, algebra students explained and
demonstrated how to identify the variables of the problem,
assign symbols to all variables, organize the data into a
matrix, represent the problem as an inequality, and then
solve the inequality. Manufacturing students constructed
a matrix, recorded proper values, and then calculated the
solution to the problem as represented in Table 3.
Upon completion of the calculations, each group discussed
and responded to the following questions:
1. When might a manufacturing engineer select a less costly
or more costly tool for an operation?
2. What workstation costs were not included in this cost
analysis? Discuss costs related to the characteristics
Tool
Operation
Time 1
(T)
(in secs)
Labor Rate 2
(R)
(per hour)
Labor Cost 3
(L) (per sec)
Labor Cost
(LC) (per
operation)
Tool Cost
(TC)
When is Labor Cost
≥ Tool Cost?
1
2
3
R / 3600
L x T
LC(N) ≥ TC
N = # of operations
1
Time = Average or mean time of three trials
2
Labor Rate = Minimal Wage
3
3600 seconds = 60 minutes = 1 hour
Table 3. Matrix of process time, labor costs, and tool costs.
10 • The Technology Teacher • April 2007