Hello I need some help with these 4 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

5. A bus service carries 10 000 people daily between Ajax and Union Station. The 5 bus company has space to serve up to 15 000 people each day. The cost to ride the bus is $20lday. Market research shows that if the fare is increased by $0.50lday, 5 then 200 fewer people will ride the bus. What fare should be charged to get a 5 maximum revenue, given that the bus company must have at least $130 000 in fares a day to cover operating expenses? " 5' e. Afarmer Wants to fence a rectangular area of scenes E m2 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 i perimeter and thus. minimize the cost of the fence? (is. Find the dimensions of the rectangutsreree that use the j n'I'nimum amount of fencing}. E T. A crocodile is stalking it's prey located 2t] metres upst on the opposite bank Ma 5 river. Crocodiles travel at different speeds :' on land and in the water. The time taken for the crocodile to reach its prey can be 5 minimised if it swims to a particular point P, x 5 metres upstream on the opposite side of the river as sheen in the diagram. The time tel-zen. T , measured in tenths of a 5 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 800m2 . She needs to nd the dimensions of the rectangular box that would contain a maximum volume if it were constmcted 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