Practice Problems H1:
1.While doing your thesis/plant design project, you and two friends find yourselves craving a fresh pizza.
You can’t spare the time to pick up the pizza and must have it delivered. “Pizza Store 1” offers a 1-1/4-
inch-thick (including toppings), 20-inch square pizza with your choice of two toppings for $15 plus 5%
sales tax and a $1.50 delivery charge (no sales tax on delivery charge). “Pizza Store 2” offers the round,
deep-dish Sasquatch, which is 20 inches in diameter. It is 1-3/4 inches thick, includes two toppings, and
costs $17.25 plus 5% sales tax and free delivery.
a. What is the problem in this situation? Please state it in an explicit and precise manner.
b. Systematically apply the seven principles of engineering economy to the problem you have defined in
Part (a).
c. Assuming that your common unit of measure is dollars (i.e., cost), what is the better value for getting a
pizza based on the criterion of minimizing cost per unit of volume?
d. What other criteria might be used to select which pizza to purchase?
(a) One problem involves how to satisfy the hunger of three students -- assume a piping hot delicious
pizza will satisfy this need. (Another problem is to learn enough about Engineering Economy to
pass -- or better yet earn an “A” or a “B” -- on the final examination and ace the course. Maybe a
pizza will solve this problem too?) Let’s use “hunger satisfaction with a pizza” as the
problem/need definition.
(b) Principle 1 - Develop the Alternatives
(i) Alternative 1 is to order a pizza from “Greenwich’s”
(ii) Alternative 2 is to order a pizza from “Pizzadoz’s”
Other options probably exist but we’ll stick to these two alternatives
Principle 2 - Focus on the Differences
Difference in delivery time could be an issue. A perceived difference in the quality of the
ingredients used to make the pizza could be another factor to consider. We’ll concentrate our attention on
cost differences in part (c) to follow.
Principle 3 - Use a Consistent Viewpoint
Consider your problem from the perspective of three customers wanting to get a good deal. Does it
make sense to buy a pizza having a crust that your dog enjoys, or ordering a pizza from a shop that
employs only college students? Use the customer’s point of view in this situation rather than that
of the owner of the pizza shop or the driver of the delivery vehicle.
Principle 4 - Use a Common Unit of Measure
Most people use “dollars” as one of the most important measures for examining differences
between alternatives. In deciding which pizza to order, we’ll use a cost-based metric in part (c).
Principle 5 - Consider All Relevant Criteria
Factors other than cost may affect the decision about which pizza to order. For example, variety
and quality of toppings and delivery time may be extremely important to your choice. Dynamics of
group decision making may also introduce various “political” considerations into the final selection
(Can you name a couple?)
Principle 6 - Make Uncertainty Explicit
The variability in quality of the pizza, its delivery time and even its price should be carefully
examined in making your selection. (Advertised prices are often valid under special conditions --
call first to check on this!)
Principle 7 - Revisit Your Decision
After you’ve consumed your pizza and returned to studying for the final exam, were you pleased
with the taste of the toppings? On the downside, was the crust like cardboard? You’ll keep these
sorts of things in mind (good and bad) when you order your next pizza!
(c) Finally, some numbers to crunch -- don’t forget to list any key assumptions that underpin your
analysis to minimize the cost per unit volume (Principles 1, 2, 3, 4 and 6 are integral to this
comparison)
Assumptions: (i) weight is directly proportional to volume (to avoid a “meringue” pizza with lots
of fluff but meager substance), (ii) you and your study companions will eat the entire pizza (avoids
variable amounts of discarded leftovers and hence difficult-to-predict cost of cubic inch consumed)
and (iii) data provided in the Example Problem are accurate (the numbers have been confirmed by
phone calls).
Analysis: Alternative A “Greenwich”
Volume = 20 x 20 x 1 ¼ = 500 in.3
Total Cost = $15 (1.05) + $1.50 = $17.25
Cost per in.3 = $0.035
Alternative B “Pizzadoz’s”
Volume = (3.1416)(10)2 (1.75) = 550 in.3
Total Cost = $17.25 (1.05) = $18.11
Cost per in.3 = $0.033
Therefore, order the pizza from “Fred’s” to minimize total cost per cubic inch.
(d) Typical other criteria you and your friends could consider are: (i) cost per square inch of pizza
(select “Greenwich”), (ii) minimize total cost regardless of area or volume (select “Greenwich”), and (iii)
“Pizzadoz’s” can deliver in 30 minutes, but “Greenwich” cannot deliver for one
hour because one of their ovens is not working properly (select “Pizzadoz’s”).
2. During your first month as an employee at Greenfield Industries (a large drill-bit manufacturer),
you are asked to evaluate alternatives for producing a newly designed drill bit on a turning machine.
Your boss’ memorandum to you has practically no information about what the alternatives are and
what criteria should be used. The same task was posed to a previous employee who could not finish
the analysis, but she has given you the following information: An old turning machine valued at
$350,000 exists (in the warehouse) that can be modified for the new drill bit. The in-house
technicians have given an estimate of $40,000 to modify this machine, and they assure you that they
will have the machine ready before the projected start date (although they have never done any
modifications of this type). It is hoped that the old turning machine will be able to meet production
requirements at full capacity. An outside company, McDonald Inc., made the machine seven years
ago and can easily do the same modifications for $60,000. The cooling system used for this machine
is not environmentally safe and would require some disposal costs. McDonald Inc. has offered to
build a new turning machine with more environmental safeguards and higher capacity for a price of
$450,000. McDonald Inc. has promised this machine before the startup date and is willing to pay any
late costs. Your company has $100,000 set aside for the start-up of the new product line of drill bits.
For this situation,
a. Define the problem.
b. List key assumptions.
c. List alternatives facing Greenfield Industries.
d. Select a criterion for evaluation of alternatives.
e Introduce risk into this situation.
f. Discuss how nonmonetary considerations may impact the selection.
g. Describe how a post audit could be performed.
(a) Problem: To find the least expensive method for setting up capacity to produce drill bits.
(b) Assumptions: The revenue per unit will be the same for either machine; startup costs are
negligible; breakdowns are not frequent; previous employee’s data are correct; drill
bits are manufactured the same way regardless of the alternative chosen; in-house
technicians can modify the old machine so its life span will match that of the new
machine; neither machine has any resale value; there is no union to lobby for inhouse
work; etc.
(c) Alternatives: (1) Modify the old machine for producing the new drill bit (using in-house
technicians); (2) Buy a new machine for $450,000; (3) Get McDonald Inc. to
modify the machine; (4) Outsource the work to another company.
(d) Criterion: Least cost in dollars for the anticipated production runs, given that quality and
delivery time are essentially unaffected (i.e., not compromised).
(e) Risks: The old machine could be less reliable than a new one; the old machine could
cause
environmental hazards; fixing the old machine in-house could prove to be
unsatisfactory; the old machine could be less safe than a new one; etc.
(f) Non-monetary Considerations: Safety; environmental concerns; quality/reliability
differences;
“flexibility” of a new machine; job security for in-house work; image to outside
companies by having a new technology (machine); etc.
(g) Post Audit: Did either machine (or outsourcing) fail to deliver high quality product on
time?
Were maintenance costs of the machines acceptable? Did the total production costs
allow an acceptable profit to be made?
