The total 10 marks: 2 marks for completion & 8 marks for 1-3 questions randomly marked. You must show all your work to get full marks. 1. A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) maximize and (b) minimize the combined area of the circle and the square? 2. Suppose you own a tour bus and you book groups of 20 to 70 people for a day tour. The cost per person is $30 minus $0.25 for every ticket sold. If gas and other miscellaneous costs are $200, how many tickets should you sell to maximize your profit? Treat the number of tickets as a nonnegative real number. 3. Two poles are connected by a wire that is also connected to the ground. The first pole is 20 ft tall and the second pole is 10 ft tall. There is a distance of 30 ft between the two poles. Where should the wire be anchored to the ground to minimize the amount of wire needed? 10 20 20 4. Evaluate the following limit: X X (a) lim x-1- x 1 In x a (b) lim 1+ - for a constant a , X+X X 30 5. Use limit methods to determine which of the two functions grows faster, or state that they have comparable growth rates. Inx; Inx 1 - 6. The demand equation for the Roland portable hair dryer is given by x = (225 p), (0 x 15), where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars. 8 and when p = 10? (a) Find the elasticity of demand function, E(p). (b) Is the demand elastic or inelastic when p = (c) When is the demand unitary? (d) If the unit price is lowered slightly from $10, will the revenue increase or decrease? Justify. (e) If the unit price is increased slightly from $8, will the revenue increase or decrease? Justify.