You are given the following data for your firm, which sells a patented super-absorbent cleaning towel for use in large retail complexes (called "One Wring to Rule the Mall" ).

Q	P	TC
0	$160	$3,000
10	$152	$3,630
20	$144	$3,990
30	$136	$4,170
40	$128	$4,260
50	$120	$4,350
60	$112	$4,530
70	$104	$4,890
80	$96	$5,520
90	$88	$6,510
100	$80	$7,950

a. Determine equations for

1-P=f(Q)

2-MR=f(Q),

3-ATC=f(Q, Q²)

4-AVC=f(Q, Q²)

5- MC=f(Q, Q²).

Recall that your marginal equations should be derivatives of your totals!

b. Determine the profit-maximizing price and quantity. (Since MC is in terms of Q², solving with calculus and algebra can be messy unless you know the quadratic formula. Your table should give an exact answer.)

Please include table for reference-

c. How much total profit would your firm earn if you set P and Q according to part b?

d. Describe the competitiveness of the market by calculating the Lerner index.