5. A bus service carries 10 000 people daily between Ajax and Union Station. The bus company has space to serve up to 15 000 people each day. The cost to ride the bus is $20/day. Market research shows that if the fare is increased by $0.50/day, then 200 fewer people will ride the bus. What fare should be charged to get a maximum revenue, given that the bus company must have at least $130 000 in fares a day to cover operating expenses? 6. A farmer wants to fence a rectangular area of 800,000 ma and divide it in half with a fence parallel to one of the sides of the rectangle. The middle fences is twice as expensive, so doubled (ie just put two fences down the middle). How can this be done in order to minimize the perimeter and thus, minimize the cost of the fence? (ie. Find the dimensions of the rectangular area that use the minimum amount of fencing). 7. A crocodile is stalking it's prey located 20 metres upstream on the opposite bank of a river. Crocodiles travel at different speeds 20 metres on land and in the water. The time taken for x metres the crocodile to reach it's prey can be P minimised if it swims to a particular point P, x metres upstream on the opposite side of the river as shown in the diagram. The time taken, T , measured in tenths of a second is given by the formula T (x) = = 5 (36+x2) +4(20-x) a) Calculate the time taken if the crocodile does not travel on land ? b) Calculate the time taken if the crocodile swims the shortest distance possible ? c) Between these two extreme there is one value of x which minimizes the time taken. Find this value of x and hence calculate the minimum possible time. 8. Sophie is given a piece of sheet metal that is twice as long as it wide. It has an area of 800m . She needs to find the dimensions of the rectangular box that would contain a maximum volume if it were constructed from this piece of metal by cutting out squares of equal area at all four corners and folding up the sides. The box will not have a lid. Give your answer correct to one decimal place