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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)=⋯

  1. Find the equations of the two tangent lines at the points x = … and x = …, respectively.
  2. 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:

  1. Determine the price and quantity at the equilibrium.
  2. Calculate the consumer surplus.
  3. Calculate the producer surplus.

Part 3

If the function is subject to the constrain

  1. Use Lagrangian multipliers method to find the critical points of the function f(x,y).
  2. Plot the function in the 3-D graph in MATLAB.
  3. 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.

  1. Find the cost of producing q1=⋯units,q2=⋯ units and q3=⋯ units per week.
  2. What do you notice? Explain your results.

Group

Part 1

Part 2

Part 3

Part 4

1

f(x)= x3-x2+1
Points: x=1 & x=2

D: p=160 e-0.04q
S: p= 20 e0.04q

f(x,y)= 3x+4y
g(x,y)=x2+y2=100
dc/dq=[0.5(0.2q2-10q)+0.3]
q1=10000;q2=15000;q3=25000