A manufacturer modelled the rate of change of the production P (in thousand) of a new toy by dP a(8-1)+20 dt (1-10)+b where is the number of months elapsed since the start of production, a and b are positive constants. It is known that the production increases to the greatest value of 8 thousand at 1= 10, and then decreases to the level as at the start of the production when /= T. Moreover, the decrease in the production from 7=25 to 7= 30 is 5 In thousand. 18 11 S (a) Find the value of a. (b) Find the value of T. (c) Express P in terms of 1. (d) Find the value of such that the rate of change of the production attains its greatest value for 0110. (Give your answer correct to 3 significant figures.)