3) The Abalone Band is planning to market their first album, Breaded Rock, on CDs and vinyl. The CD costs $1.23 each to produce, and the vinyl is $3.29 each. According to the latest economic model, if the CD sells for p dollars, and the vinyl sells for q dollars, then the demand functions will be given as r = 30000 - 1480p + 600q (for the CDs) y = 21000 + 300p - 922q (for the vinyls) a Show that the profit function (as a function of p and q) will be: P(p, q) = 30833.4p + 23295.38q - 1480p2 - 922q2 + 900pq - some constant (Note: the constant is unimportant for our purposes because we will be taking derivatives of P.) b) Show that the maximum profit is reached when p = $16 and change, and q = $20 and change