Mathematics Matlab

• To solve the questions below you need to use ONLY Matlab or mathematica

Project :The demand function for a monopolist’s product is and the average cost per unit for producing units is , where = price, and = quantity demand.

Questions
1. Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences.
2. Develop a 2D plot for demand versus the price. What do you notice?
3. Develop a 2D plot for total cost versus the quantity; average cost versus the quantity; marginal cost versus the quantity; and marginal revenue versus quantity on the same graph. What do you notice?
4. Compute the demand elasticity when price equal to 4. Interpret your result.
5. Find the quantities that maximize the total revenue and profit. Interpret your result.
6. Find the quantity that minimize the total cost function. Interpret your results.
7. Discuss the results of 6 and 7.
8. What is the price that maximizes the profit? Interpret your result.
9. What is the maximum profit? Explain clearly your result.
10. Provide a simple conclusion that would explain what you have learned during the group project. Each of the member of the selected team must relate his/her own experience in the conclusion.