It is given that at least 250 students join the picnic and the budget for booking the coaches is $2700. Mrs Lee decides to book 3 coaches of type A and x coaches of type B. (a) By considering the number of students joining the picnic and the budget for booking the coaches, set up two inequalities in x. (b) At most how many coaches of type B can be booked? (c) (i) At least how many coaches of type B should be booked? (ii) If the least number of coaches of type B is booked, find the total booking fee