Discuss the below:
Quantitative Methods
Q1: The Manager of a firm believes that the Total Revenue curve for her product varies with the quantity produced (which we will take to be quantity sold) such that it is a concave equation and that Total Revenue is zero when the quantity is 0 and also when the quantity produced is 51. At what quantity produced will Total Revenue be maximized? Explain your reasonings clearly.
Q2: The manager of a manufacturing plant has to decide what amounts of two inputs ( X1 and X2) should be purchased. The manager's budget has been predetermined by the head office. It is 60 million dollars. The price of each unit of X1 is 2 million dollars while the price of each X2 is 6 million dollars. The manager has as her aim the maximization of output. The manager knows that the level of output depends only upon the amounts of those two inputs used and that the ‘production function' is Cobb-Douglas in form. The manager also knows that the elasticity of output with respect to X1 is 1.0 and the elasticity of output with respect to X2 is 0.5.
Given that the manager's aim is to maximize output, subject to the constraint in the form of the total budget to be spent on those two inputs, what quantities of X1 and X2 should be purchased?
(As a side note, how would this differ if the elastic ties were the same)