(a) A farmer needs to build a rectangular pen that has a total square footage of 1,500,000 square feet. But, the pen has a fence that runs down the middle parallel to one of the sides. Find the dimensions (length and width) of the pen that uses the least amount of total fencing. Be sure to clearly label your dimensions and prove your answer. (b) Juno makes and sells bicycles. He sells 20 bicycles a week at $400 each and it costs him $200 to make each bike. He notices that for every $10 reduction in price, he will sell 2 more bicycles per week. (a) Find the demand function, assuming it is linear. (b) How many bicycles must he sell per week to maximize his profit? (c) What should the selling price be for the bicycles to maximize his profit? Set up 8. solve the problem using the ideas of section 4.7 & prove your