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 a 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 = 9600 − 30. Construct the revenue function, for your product. Independently of part 2, 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 1,000 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.