Find the minimizing for x and y - confirm that the second

Question

Question 1. The total weekly revenue (in dollars) that a company obtains from selling goods x and y is:

R(x,y) =  -(1/4)x² - (3/8)y² - (1/4)xy + 300x - 240y

The total weekly cost attributed to production is

C(x, y) = 180x + 140y + 5000

Find the profit maximizing levels of x and y and check the second order conditions.

Question 2. A firm's costs of plant operation are a function of two variables, x and y. The cost function is given by:

c(x,y)= 3x² - 2xy + y² +4x -F 3y

Given the solution to the first order conditions and confirm that the solution minimizes the cost function. Question 3. Find the maximizing values of (x,y) for the following function, and confirm that the second order conditions are satisfied.

f (x, y) = a ln x + bln y - 1/2c(x² + y²)

Question 4. Consider the following problem. Minimize f(x, y) - a)² + (y -b)² - 1/2 cxy.

(a) Find the minimizing for x and y.

(b) Confirm that the second order conditions are satisfied. Let f'(a, b, c) be the value of the function at the solution.

(c) Find ∂f*(a,b,c)∂u and ∂f*(a,b,c)/∂c.