NOTE: USE LINGO ONLY!!

5. (15 marks) A large retailing business has a massive distribution centre. Though it's open 24 hours per day, road construction in the area prevents all but essential supplies entering or leaving except for the one hour period from 3 am to 4 am. They therefore wish to maximize the number of trucks which can exit the centre during this time. Each transport has a length of 18.5 metres, and the front of each truck must stay a safe distance behind the back of the truck ahead of it. Where a truck travels at a speed of s km/hour, the minimum safe distance in metres for nighttime driving used by the company on its property is: 1.5 +2s +.0352 For example, if two trucks are travelling at 30 km/hour, the minimum safe distance is 1.5+2(30) +.03(30)(30) = 88.5 metres. Transport trucks exit the distribution centre on several roads, but these merge to form a single lane exit from the centre. After leaving the centre the trucks will enter a multi-lane highway. The company has imposed a speed limit of 50 km/hour on its property. (a) Formulate an algebraic model in which the truck speed s (in km/hour) and the distance d (in metres) from the front end of one truck to the front end of the next truck are the only variables. The model will be of the form max f(s,d) subject to two constraints. (b) Solve this model using LINGO (c) State how many trucks can leave per hour, the speed of each truck and the distance d