6.15 In planning for production of two products, company Z estimates expected profit to equal P: P = a(1 - e-$1*1 - BIXie-$1*1) + a2(1 - e-$2*2 - B2xze-$2*2) + a3(1 - e-B3*1*2) - X1 - X2 where x, is the amount of money spent to produce and advertise product 1, x, is the amount of money spent to produce and advertise product 2, and the a;'s and Bi's are specified constants. P, x, and x, are in units of 105 dollars. Find the maximum of P and the optimal values of x, and x, under the following conditions: a. a1 = 3, a2 =4, a3 = 1, B1 = 1.2, B2 = 1.5, and B3 = 1. b. a = 3, a, = 4, 03 =-1, B, = 1.2, B2 = 1.5, and B3 = 1