Please provide relevant solutions to the following questions

2. (20 points) Suppose the total cost function of a monopoly firm is: TC(q)= q3 - 61.25q2 +1528.5q +2000 Suppose the revenue function for the firm is: R(q)= 1200q-2q2. With this information, answer the following questions: a. (5 points) Given the form of the revenue function, derive the inverse demand function for this monopolist. Also draw the graph for the demand function. b. (2 points) Form the firm's profit function for this monopolist. c. (10 points) Solve for the firm's profit maximizing output. For full credit it is absolutely necessary to show all the numerical work. d. (3 points) What is the profit at the profit maximizing output? 3. (15 points) Suppose the total cost function of a monopoly firm is: TC(q)= q3 - 61.25q2 +1528.5q +2000 a. (3 points) Derive the expression for the average variable cost (AVC) for this firm. b. (10 points) Solve for the firm's output where the AVC is minimum. For full credit it is absolutely necessary to show all the numerical work. c. (2 points) What is the AVC at this level of output?3. True or False? Explain. (a) The utility function given by U(A, B) = (A 3)2 represents pref- erences consistent With the six assumptions about preferences as dis- cussed in class. (b) The utility function given by u(:1:1,:122) = as? | 3:2 represents prefer- ences consistent with the six assumptions about preferences as dis cussed in class. 2. It is a hot day, and Sally is very thirsty. She finds a soda machine and discovers that it only takes only quarters and dimes. Sodas are $0.85, but each requires exactly three quarters and a dime. No other combination of coins will work. Sally wants as many sodas as possible. (a) Represent Sally's preferences over quarters and dimes in a graph. Draw at least two indifference curves. Write down a utility function that would represent her preferences over quarters and dimes {not sodas]. (Assume for simplicity that quarters1 dimes and sodas are innitesimally divisible; that is, Sally can consume 0.5 cans if she has 1.5 quarters and 0.5 dimes}. (b) Sally notices that there is a nearby gas station where she can get change. That isI she can convert any coins she has into any other combination of coins with the same value. Represent her preferences over quarters and dimes in a graph. Draw at least two indifference curves. Write down a utility function that would represent her pref- erences over quarters and dimes