The total cost function of a monopolistic producer of two goods is TC = 2x + xy + 12y where x and y denote the number of units of good 1 and good 2 respectively.

If P₁ and P₂ denote the corresponding prices then the demand function of each good is P₁ = 80 - x + y and P₂ = 50 + 2x - y

Note: Type all your results with integer values without thousands symbols.

a) Calculate the values of x and y that maximize profit if the company is contracted to produce a total of 600 goods.

x = 12

y = 30

b) Calculate the maximum profit corresponding to the previous values of x and y.

Maximum profit = 1764

c) Calculate the value of Lambda (Lagrange multipliers method)

Lambda = Blank 4

d) Calculate the decrease of profit in absolute value when the production output decreases by 3 units

Decrease of profit = Blank 5