Posted: September 13th, 2017

Marginal Analysis to Business Operations

Paper, Order, or Assignment Requirements

Math 202 Category W Writing Assignment
Part 1：Suppose you start your own business. Determine a product your business will manufacture or produce. Ideally, the chosen product will 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 $15 and $310.
Part 2：Suppose total fixed costs including rent and utilities for your business are $7,500 per month. Using the cost per unit that you determined in part 1, construct a linear cost function, , for your product. Suppose you can afford $150,000 in total costs per month, how many units can you produce?
Part 3：
Let represent the quantity of units of your product demanded each month and let represent the price per unit which you sell the product in dollars. Let the price – demand equation be . Construct the revenue function, , for your product. 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). Next, find the profit function, . Determine the break – even points and interpret your results.
Part 4
：Suppose your company is currently producing 1,000 units per month. Determine the marginal cost and marginal revenue at a production level of units and interpret the results. 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.
Report
：Type a report to summarize your results from the above four parts. The report should include all calculations with explanations and/or interpretations. Also include in this report, a brief summary on the importance of marginal analysis to business operations.
This assignment is worth 70 points.