MATH221 Business Mathematics II
Group Project
Instructions
- Students are required to organize themselves in group. The Group size can be up to a maximum of four (4) students.
- Once organized, the group members HAVE to self-enroll in the groups created on Blackboard.
- Each group should select one specific project from the list below (in other words, two groups CANNOT work on the same project): First come first served!
- You need to use the provided template (available on Blackboard) to write the report.
- To solve the questions below you need to useMatlab, which is available in the computer lab.
- If you want to useMatlabon your computer (interactive use through Citrix cloud), you will find on Blackboard the instructions on how to get it.
- I am available during office hours to answer your questions regarding the project questions and Matlab
Part 1
For the function f(x)=⋯
- Find the equations of the two tangent lines at the points x = … and x = …, respectively.
- Find the intersection point of the two tangent lines, if any.
Part 2
Consider the following demand, supply and total cost functions:
Demand function: …
Supply function:
- Determine the price and quantity at the equilibrium.
- Calculate the consumer surplus.
- Calculate the producer surplus.
Part 3
If the function is subject to the constrain
- Use Lagrangian multipliers method to find the critical points of the function f(x,y).
- Plot the function in the 3-D graph in MATLAB.
- Using Matlab function “ fmincon”, find the maximum and minimum of the function f(x,y).
Part 4
Suppose that a restaurant has certain fixed costs per month of $5000. The fixed costs could be interpreted as rent, insurance etc. The marginal cost function of the restaurant is given by:
dc/dq=⋯
where c is the total cost in dollars of producing q units of good per week.
- Find the cost of producing q_{1}=⋯units,q_{2}=⋯ units and q_{3}=⋯ units per week.
- What do you notice? Explain your results.
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Group |
Part 1 |
Part 2 |
Part 3 |
Part 4 |
1 |
f(x)= x^{3}-x^{2}+1 |
D: p=160 e^{-0.04}q |
f(x,y)= 3x+4y g(x,y)=x^{2}+y^{2}=100 | dc/dq=[0.5(0.2q^{2}-10q)+0.3] q_{1}=10000;q_{2}=15000;q_{3}=25000 |