The performance function for a highway connecting a suburb with the business district can be represented by a straight line of the form t = a + bp, where t is the travel time in minutes, q is the traffic flow in vehicles per hour, and a and b are constants equal to 15 minutes and 0.01 minute/vehicle-hour, respectively. The demand function, also represented by a straight line, is q = c - dt, where cand d are constants equal to 6000 vehicles/hr and 150 vehicles/hour/minute, respectively. (a) Find the equilibrium flow (q*) and the corresponding equilibrium time (t*) algebraically, and sketch the functions. (b) If the length of this highway is 25 miles, what is the average speed of vehicles along this highway? (c) It is proposed to improve this highway such that constant b is now 0.005. What would be the new values of t* and q* and what would be the average speed on this highway?