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Math 202 Marginal Analysis Writing Assignment

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 for all values with units labeled appropriately.

Papers should be 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).

This paper is due Friday, June 9th. If your paper is submitted by the early deadline

(Wednesday June 7th) you will receive 10 points extra credit on the paper and if it is

submitted by the late deadline (Monday June 12th), you will receive a 10–point penalty on

the paper. No papers will be accepted after the late deadline. No exceptions. Papers must be

submitted as hardcopy submissions and as a word document via email by the deadline. The

paper copy may be submitted during class or to the instructor’s mailbox. The paper itself is

worth 80 points. The remaining 20 points can be easily obtained by scheduling a 2 to 3-

minute meeting with me by Friday June 16th. I will ask you some basic questions on your

paper to make sure the work you did is original.

The paper should be typed using Microsoft Word, with a Cambria Math 12 pt font, 1.5

spaced. It should be at least 2 pages long in default Word margins. Graphs can be

screenshotted from online graphing tools, although it is preferable that they be done using

Excel’s graphing tool. Equations must be written using the Equation Editor in word as I will

demonstrate in class. For example, “f(x) = x^2, 3/x…” is not acceptable. You should use the

equation editor to get � � = �`,

a

b … If you need help using word or if you have specific

questions regarding the paper, you may ask me, Jillian (the class TA) or an MLC tutor.

Prompt

Suppose you start your own business. Determine a product your business will manufacture

or produce. The chosen product must be a general description, for example a smartphone,

and not a specific brand or item, for example an iPhone 6. Do some informal research to

determine a reasonable cost of producing one unit of the product. The restriction on this is

that the cost per unit must be between $20 and $270.

Suppose total fixed costs including rent and utilities for your business are $3750 per

month. Using the cost per unit that you determined, construct a linear cost function, �(�),

for your product.

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. Let the price – demand

equation be � = �(�) = 14500 − 50�. Use �(�) to determine the feasible range of units

demanded per month (i.e. what is the smallest number of products you could feasibly sell

and what is the largest number of products you could feasibly sell in a month). Construct

the revenue and profit functions, � � and � � , for your product. Determine the breakeven

points and interpret your results. What production levels will cause your company to

make profit? What production levels will cause your company to incur a loss?

Suppose your company is currently producing 3,700 units per month. Determine the cost,

revenue, and profit at 3,700 units. Determine the marginal cost, marginal revenue and

marginal profit at a production level of 3,700 units and interpret the results.

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

product if demand is 3,700 units per month?

Write a function for the elasticity of demand �(�) and determine whether the demand is

elastic, inelastic, or has unit elasticity at the unit price you found for the demand of 3,700

units. Use what you have found about elasticity to 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, should you increase or decrease production from 3,700 units

to maximize profit? Justify your answer by including what information you’ve collected so

far that lead you to your conclusion.

Finally, plot your profit function and determine the optimal production level that will

maximize profits and explain why you know this using an algebraic method and a graphical

method. What is the maximum profit that your company could achieve? 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 summary on the importance of marginal analysis to business operations

& how you might apply these concepts in the future.