14. [6 marks] After a new product has been launched onto the market, its sales volume is given by S = (AT + 300) (A + 72)-1/2, where T = time (in months) since the product was first introduced and A = amount (in hundreds of dollars) spent monthly on advertising. (a) Determine the partial derivative of sales volume with respect to advertising, aA as (b) Suppose advertising is fixed at $9000 per month [i.e., A = 90]. Determine when the monthly sales as volume will begin to decrease, given that aT = (A2 - 3007) (A + 12) -3/2