calculus

Derivatives of Polynomials Discussion Board

One common business variable is the net profit margin (NPM). The NPM is the net profit divided by revenue. It shows the profit in dollars as a ratio to the revenue in dollars.

Part I:  Why would this be important to business owners and analysts?

Part II:  The American ChainMail Corporation has net profits given by the function

P(x) = -.1x^2 + 100x – c   ( THE COST IS 450 IN HUNDREDS)

in hundreds of dollars, where x is the number of full suits of armor sold. Each full suit of armor costs $5,000.  The revenue function is R(x) = 50x, (not R(x) = 5000x, since the revenue
function must also be in hundreds of dollars). Complete the profit function by choosing a constant from the following:

If your last name starts with the letter…     Choose a fixed cost between…

A-F                                                                   5000-10000

G-K                                                                  15000-20000

L-N                                                                  25000-30000

0-R                                                                   35000-40000

S-U                                                                   45000-50000 (use these numbers)

V-Z                                                                  55000-60000

NOTE: The value of c will actually be negative in the above function.

Label your first post with your last name and your assigned figure for P so that your classmates immediately know the basis of your calculations (e.g., Brook c = 7500, but Brook would use c = 75 in the profit function above since this function is in hundreds of dollars; i.e., p(x) = -0.1x^2 + 100x -75

Part III:  Build the function for the net profit margin, NPM (x) = P (x)/R(x), and apply the

quotient rule to find the rate of change when 40 suits of armor are sold. Then, estimate the

number of suits of armor that need to be sold so that the NPM is increasing at a rate of 10%. Please round your answer to the nearest whole suit of armor.