## Wolfarm Mathematica

Wolfarm Mathematica

Projects List

Project #1: The demand function for a monopolist�s product is ????=700?2???? and the average cost per unit for producing ???? units is ?????=????+100+ 1000???? , where ????= price, and ????= quantity demand.

Project #2: Consider the demand function is ????=10000?80???? and the total cost function is ????=0.004 ????3+20 ????+5000.

Project #3: The demand function for product is ????=?????+108 and the total cost per unit for producing ???? units is ????=3????2+8????+300 , where ????= price, and ????= quantity demand.

Project # 4: The demand function for product is ????=?5????+4500 and the total cost per unit for producing ???? units is ????=3????2+300????+20000 , where ????= price, and ????= quantity demand.

Project # 5: Suppose that the cost function for a product is given by ????(????)=0.05????2?10????+1000. The demand function for product is ????=?5????+200.

Project #6: Suppose that the dollar cost of producing q appliances is ????(????)=500?100????+0.4????2 and the demand function is given by =20?0.02???? .

Project #7: Suppose that the dollar cost of producing q appliances is ????(????)=1500?90 ????+0.3????2 and the demand function is given by ????=25?0.02????

Project #8: The demand function for a monopolist�s product is ????=800????? and the average cost per unit for producing ???? units is ?????=????+100+ 500???? , where ????= price, and ????= quantity demand.

Project #9: The demand function for a monopolist�s product is ????=800?10???? and the average cost per unit for producing ???? units is ?????=????+10+ 1100???? , where ????= price, and ???? = quantity demand.

Project #10: The demand function for a monopolist�s product is ????=800?10???? and the average cost per unit for producing ???? units is ?????=????+100+ 1300???? , where ???? = price, and ???? = quantity demand

Questions

Use of MATHEMATICA software is recommended . Choose any of the projects and answer the question for your selected project at the end of this document.

1. Develop a 2D plot for demand versus the price.

2. Develop a 2D plot for average cost versus the quantity.

3. Compute the demand elasticity when price equal to 1.

4. Compute the marginal cost when the quantity is equal 1.

5. Develop the profit function.

6. Develop 3D plot for profit function versus price and quantity.

7. Find the quantity that maximizes the total profit.

8. What is the price that maximizes the profit?

9. What is the maximum profit?