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 selfenroll 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 3D 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.
Group

Part 1

Part 2

Part 3

Part 4

1

f(x)= x^{3}x^{2}+1
Points: x=1 & x=2

D: p=160 e^{0.04}q
S: p= 20 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

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