Math 202 Writing Prompt (2) (2)

Math 202 Writing Prompt (2) (2) - Math 202 Marginal...

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Unformatted text preview: 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. 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 assignment is worth 100 points and is due Monday, Nov. 28 by 5pm. If your paper is submitted by the early deadline (5pm Wed, Nov. 16) you will receive 10 points extra credit. If your paper is submitted by the late deadline (5pm Wed, Nov. 30) you will receive a 10-­‐point penalty. No papers will be accepted after November 30. Papers should be reasonably formatted and will be submitted online through MyMathLab writing space. You do not need to attach your scratch work. Prompt Suppose you start your own business. Determine a product your business will manufacture or produce. The chosen product should be a general description, for example a smartphone, 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 $10 and $140. Suppose total fixed costs including rent and utilities for your business are $4000 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 ! = !(!) = 12000 − 75!. 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 break – even points and interpret your results. Suppose your company is currently producing 3,000 units per month. Determine the cost, revenue, and profit at 3,000 units. Determine the marginal cost, marginal revenue and marginal profit at a production level of 3,000 units and interpret the results. According to the price – demand equation, at what unit price are you selling your product if demand is 3,000 units per month? Write a function for the elasticity of demand ! (!) and determine whether the demand is elastic, inelastic, or has unit elasticity at this price. Discuss how increasing or decreasing the price would affect the revenue. Based on the analysis you have done so far, should you increase or decrease production? Justify your answer. Finally, determine the optimal production level that will maximize profits and explain why you know this. What is the maximum profit? Determine the revenue and cost for the optimal production level. At 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. ...
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