Free Essay About Math 202 Category W Writing Assignment

Part 1

Introduction.
Based on the current economic situation and the desired quality, the production cost is estimated as; direct material= $15 and direct labor = $5. The unit production cost is:

Part 2:

If the fixed costs are $7500; the cost function for our headphones is;
Cx=20x+$7500

Where x is the number of headphones produced.

With a budget of $ 150,000, the number of headphones that I can produce is calculated as follows;
$150,000=20x+$7500 = 150,000-750020 = 7125 headphones.

Part 3

If the price-demand equation is x= 9600-30p. The revenue function R(x) = unit price × quantity sold = xp
But x= 9600-30p thus the revenue function is;
Rx=9600-30pp
=9600p-30p2
Profit function P(x) = Revenue – cost
px=9600p-30p2-20x+$7500=9600p-30p2-209600-30p+7500=9600p-30p2-192,000+30p-7500=9600p-30p2-199500
At break-even point profit = 0

Therefore

9600p-30p2-199500=0
Solving this quadratic equation gives p= $297.7 or p= $22.34. The recommended range is p=$22.34.
Thus break even units, x = 9600-30(22.34) = 8929.8 = 8930 (approximate)

Part 4

At a production level of 1000 units;
Marginal cost is the cost of producing an extra unit of the headphones. Marginal cost is the first derivative of the cost function.
Given Cx=20x+$7500
Marginal cost = ddxCx=20

Thus at a production level of 1000 units

Marginal cost = $20

The approximate cost of producing the 1001st headphone is $20

Marginal revenue is the first derivative of the revenue function.
R(x)=9600p-30p2
Marginal revenue = $22. 43

Thus the approximate revenue from the sale of the 1001st head phone is $22.43

Profit is maximized when marginal cost = marginal revenue.
That is at the point where 9600 - 60p=20
p= 160
But from x= 9600-30p
Profit are thus maximized at x= 9600-(30*160)= 4800 units.
Based on the analysis so far, the productions should be increased. This is because the break-even point is at 8930. At a production level of 1000 units the company will be incurring losses.

Importance of marginal analysis to business operations:

In making business decisions business aim at the maximization of profit. Marginal analysis guides businesses in evaluation of decisions so as to balance between benefits and costs of additional actions e.g. whether to manufacture more units of a product or not. Marginal analysis helps determine if the benefits will be more than the costs thus increasing the profits of the firm.