Instructions:

Your assignment is to write an original report that gives essay – style answers to the

questions posed below. Be sure to address every point of discussion. The report should

include explanations and interpretations when requested. You should label units when

appropriate. Papers should be typed and reasonably formatted and should read as an

essay

and not a list of equation and values. You do not need to include your

scratch work or

calculations, but you should include any equations or functions that you are asked to

compose

as part of the prompt. Your conclusions should make sense in the context of the

scenario and

should be consistent throughout the paper (make sure you don’t contradict yourself).

Submission Instructions:

You are required to print a copy of your paper and submit to your instructor

before or after

class or to your instructor’s mailbox by the deadline. Please staple multiple pages

together.

In addition to the submitted hardcopy, you are required to submit an

electronic version of

your paper. Email your paper by the deadline to the instructor’s email address.

Please save the file using the following template:

(last name).(first name).(section number).docx

For example: morgan.mindy.7.docx

This assignment is worth 100 points and is due Wednesday, April 11 by 5pm. If your

paper is

submitted by the early deadline (5pm Friday, April 6) you will receive 10 points extra

credit. If

your paper is submitted by the late deadline (5pm Monday, April 16) you will receive a

10-

point penalty. Papers will not be accepted after April 16, no exceptions.

Additional Sources:

You will be asked to graph certain functions. You may do this using an

online graphing utility

such as the Desmos graphing calculator (desmos.com). Please be sure to adjust the

axes to

match the domain of the revenue function and include the entire graph. Prompt:

Suppose you start your own business. Select a product your business will produce that could

be reasonably manufactured for your assigned variable cost per unit. The chosen

product

must be a general description, for example a smartphone, and not a specific brand or item, for

example, do not choose an iPhone 6. Use your assigned variable cost and assigned fixed cost

to

construct a linear cost function �(�) to describe the total monthly cost for your

business.

Let � represent the quantity of units of your product demanded each month and let

�

represent the price per unit at which you sell the product, in dollars. Use your

assigned price –

demand equation to construct the revenue function �(�) to describe your company’s

total

monthly revenue. Then determine the domain of the revenue function which represents the

feasible range of units that could be produced.

Construct the profit function �(�) to describe your company’s total monthly profit. Determine

the break-even points. What production levels will cause your company to make profit? What

production levels will cause your company to incur a loss? Include a graph of the

revenue and

cost functions to support the break-even points that you found and label the break-even

points on your graph using coordinates.

Now choose a monthly production level that is within the domain of the revenue function

that

you found. You can select this production level without using further analysis. Determine

the

total cost, revenue, and profit at your chosen production level. Then determine the

marginal

cost, marginal revenue and marginal profit at your chosen production level and interpret

each

of these values.

According to the price – demand equation, at what unit price ($�) are you selling your

product

if demand is at your chosen production level? Write a function for the elasticity

of demand

�(�) (be sure to include this function in the paper). Use �(�) to determine whether the

demand is elastic, inelastic, or has unit elasticity at the unit price you found for

the demand at

your chosen production level. Discuss how increasing or decreasing the price would affect

revenue. What unit price would result in unit elasticity?

Based on the analysis you have done so far and without calculating the optimal production

level that you will find in the next part, determine whether you should increase or

decrease

production from your chosen production level in order to maximize total profit. Justify your

answer by including what information you’ve collected so far that lead you to your

conclusion.

Determine the optimal production level that will maximize profits and find the maximum

profit that your company could achieve. Show that you have found the maximum profit in two

ways: algebraically and graphically.

Determine the revenue and cost at this optimal production level. Use the price – demand

equation to determine what price should you sell each unit so that you can maximize

profit.

Draw some conclusions about your business’s optimal operations. You should conclude your

report with a brief summary on the importance of marginal analysis to business

operations &

how you might apply these concepts in the future.Your grade will be evaluated on

the following:

• Completion

• Accuracy

• Format

• Grammar

• Interpretation of values

• Consistency

• Following directions for student chosen values

• Labeling units properly and appropriately

Calculation Tips:

• Do not use intermediate rounding during calculations to avoid rounding errors. Round

at the very end, only if appropriate.

o Example: when working through a calculation such as

5 + ,250 − 4 117 3 5 (6)

37

you should simplify under the radical to obtain

5 + ,250 − 72 17

37 =

5 + ,4178 17

37

then you should round at the very end to obtain

5 + ,4178 17

37 = 0.56

o Intermediate rounding will lead to rounding errors such as:

5 + ,250 − 4 117 3 5 (6)

37 =

5 + √205.43

37 =

5 + 14.33

37 =

19.33

37 = 0.52

and it not as accurate as we would like you to be.

o Example: if you are describing a value in terms of dollars, we typically

round to

the hundredth decimal. So instead of stating $<=>

?@

, you should write $6.77

• Use exact form whenever possible.

o Example: use the exact value A?

@

instead of the decimal approximation 1.86 when

writing functions or working through calculations requiring irrational numbers.

o Keep in mind that for numbers such as A

<

= 0.5 or ?

=

= 0.6, you can use either the

decimal or the fraction form since these are rational values and using the

decimal form will not affect any rounding errors.