# Group Project MATH 221, Spring 2015.

| May 19, 2015

Group Project MATH 221, Spring 2015.

Instructions
? Students are required to organize themselves in group.
? Once organized, the group members HAVE to sign-up in the groups created on Blackboard. The group number should correspond to the project number (you select from the list below). For example, the students who select project one should sign-up in group one on blackboard.
? The Group size can be up to a maximum of 5 students.
? Each group is required to select a project from the following list.
? Only one group can work on a specific project (in other words, two groups CANNOT work on the same project).
? All projects are subject to the same set of questions listed at the end.
? The report on the project shall be due one week before the end of classes.
Thursday, May 28th , 2015
Submission location:
Blackboard AND hard copy submission
Submission format:
1. Use the provided template
2. Printed report
3. Word file
Group size
Max. 5
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?

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