1. 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" 9). Q P TC 0 $26.00 $180.00 10 $25.25 $288.00 20 $24.50 $395.00 30 $23.75 $504.00 40 $23.00 $618.00 50 $22.25 $740.00 60 $21.50 $873.00 70 $20.75 $1,020.00 80 $20.00 $1.184.00 90 $19.25 $1.368.00 100 $18.50 $1.575.00 a. Determine equations for P=f(Q), VIR=f(Q), ATC=[(Q. Q3), AVC=f(Q, Q3), MC=f(Q. Q'). 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 Q , solving with calculus and algebra can be messy. Your table should give an exact answer.) Rectangu 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