Woodhead's is a microbrewery in the Pittsburgh area. They would like to optimize the profit from a new beer. If x units of malted barley is used to craft this new beer, they estimated that they will be able to produce a 2 ln(4x) pitchers of beer where a is a constant (they don't want to reveal data related to the efficiency of their process, so a is not given to us). They have already committed to use at least 1 unit of malted barley, i.e., we need to consider the case of x 1 only. For every unit of malted barley, they expect to incur a procurement and production cost summing up to $5. Moreover, they plan to sell each pitcher of this new beer for $12. Because of the high demand, they expect that all of the beer they offer will be sold. How much malt should Woodhead's use in their production in order to maximize their total profit? Note that the total profit of Woodhead's is their total revenue minus their total cost (including both production and procurement costs). 1. Write down the objective function f(x) for this problem. 2. Use the derivative f (x)