Reference no: EM132278497

Business Mathematics Assignment - Project

Part 1 - For the function f(x) = x³ - x + 1

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

b) Find the intersection point of the two tangent lines, if any.

Part 2 - Consider the following demand, supply and total cost functions:

Demand function: p = 50e^-0.05q

Supply function: p = 5e^0.03q

a) Determine the price and quantity at the equilibrium.

b) Calculate the consumer surplus.

c) Calculate the producer surplus. 

Part 3 - If the function f(x, y) = 3x + 2y is subject to the constrain g(x, y) = x² + y² = 100.

a) Use Lagrangian multipliers method to find the critical points of the function f(x, y).

b) Plot the function in the 3-D graph in MATLAB.

c) 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 = [0.64(0.17q² - 32q) + 0.75]

where c is the total cost in dollars of producing q units of good per week.

a) Find the cost of producing q₁ = 11750 units, q₂ = 17900 units and q₃ = 26300 units per week.

b) What do you notice? Explain your results.