# Algebra4 19 21

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Subject
Algebra
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cabrillo high school
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Production Schemes
Worksheet
Piecewise Defined Functions, Modeling, Domain/Range
Your company has three factories that are located in Wichita, Kansas, Seattle, Washington, and Omaha,
Nebraska. Each site produces the same consumer product, but each has a different set of advantages
and disadvantages. Therefore, the cost schedule for producing a given number of units is different for
each plant. All of the unit numbers are for daily production runs. The company receives orders from
its retailers on a just-in-time inventory model, so we will assume that the entire order must be filled on
the day it is ordered.
For each factory, you must first consider the special circumstances and how its cost function is affected.
As the company’s production analyst, your goal is to use your knowledge of the three plants to decide
how each day’s orders should be manufactured so that the company’s overall cost per unit is minimized.
Directions:
Complete each of the following tasks, reading the directions carefully as you go. Be sure to show all work
where indicated and to insert images of graphs when needed. Make sure that all graphs or screenshots
include appropriate information, such as titles and labeled axes. Use the built-in Equation Editor to type
equations with mathematical symbols that cannot be typed from the keyboard.
into this document so you can submit it to your teacher for a grade. You will be given partial credit based
on the work you show and the completeness and accuracy of your explanations.
the document, e-mail it to your teacher, or hand in a hard copy.

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Worksheet (continued)
1. Factory in Wichita
The cost per unit for Wichita’s factory is graphed as a piecewise function over the domain [0, 35000].
a. Write one or two sentences to describe the cost function for the Wichita factory. (5 points)
In Wichita’s factory, the cost per unit for production is \$1.0 when we produce less than or
equal to 25000 units. If we produce more than 25000 units, but less than or equal to 35000
units, the cost per unit for production is \$0.8.
b. Write the piecewise function for the cost per unit for production of units in the Wichita factory.
That is, state the function
, where is the number of units produced. (10 points)


c. What is the cost per unit for 35,000 units? (5 points)
Using the state function, the cost per unit for 35000 units is \$0.8.
d. According to the graph, if only one unit was produced, the cost per unit would be \$1.00. In reality,
the company would not call in its worker and start up the equipment to produce one unit. What
safeguard do you think that many manufacturers use to avoid this type of problem? (5 points)
Manufacturers usually set the minimum number of units that can be ordered by a customer.
This can be determined by making use of the cost-benefit analysis.

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Production Schemes Worksheet Piecewise Defined Functions, Modeling, Domain/Range Your company has three factories that are located in Wichita, Kansas, Seattle, Washington, and Omaha, Nebraska. Each site produces the same consumer product, but each has a different set of advantages and disadvantages. Therefore, the cost schedule for producing a given number of units is different for each plant. All of the unit numbers are for daily production runs. The company receives orders from its retailers on a just-in-time inventory model, so we will assume that the entire order must be filled on the day it is ordered. For each factory, you must first consider the special circumstances and how its cost function is affected. As the company’s production analyst, your goal is to use your knowledge of the three plants to decide how each day’s orders should be manufactured so that the company’s overall cost per unit is minimized. Directions: Complete each of the following tasks, reading the directions carefully as you go. Be sure to show all work where indicated and to insert images of graphs when needed. Make sure that all graphs or screenshots include appropriate information, such as titles and labeled axes. Use the built-in Equation Editor to type equations with mathematical symbols that cannot be typed from the keyboard. You will be graded on the work you show, or on your solution process, in addition to your answers. Make sure to show all of your work and to answer each question ...
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