A principle in economics states that profit is maximized at the value (number of products sold) that makes marginal revenue equal to marginal cost, the derivatives of the revenue and cost functions, respectively. In this discussion you will verify this principle with an example of your own making. Choose a negative integer and let it be represented by " a\". Then choose a positive integer and represent it by " b". Note: IT IS IDEAL IF THE VALUE OF b IS MUCH GREATER THAN THE ABSOLUTE VALUE OF a. Finally, choose a negative integer and represent it by " " (any negative integer is fine). Next, substitute these values into the following equations to come up with specific profit, revenue, and cost functions: P(,\\'] =ax'+ by +c R(x)=ax?+c C (,\\) =bx b (A): Determine the x-value of the maximum of P(.\\') using the formula x= 2 Find the marginal revenue and marginal cost functions, set them equal to each other and solve for x a . Do you get the same result? (B): We have seen that an application of differential calculus is to optimize functions. Find the derivative of your profit function, set it equal to 0 and solve for x. Do you get the same result as in part (A)