A firm produces two commodities, A and B. The inverse demand functions are:

pA =9002x2y, pB =14002x4y

respectively, where the firm produces and sells x units of commodity A and y units of commodity B. Its costs are given by:

CA =7000+100x+x^2 and CB =10000+6y^2

where A, a and b are positive constants.

(a) total profit: (x,y)=3x^2 10y^2 4xy+800x+1400y17000.

(b) Assume (x, y) has a maximum point. - x=100, y=50

(c) Due to technology constraints, the total production must be restricted to be exactly 60 units. - x=40, y=20

(d) Report the Lagrange multiplier value at the maximum point and the maximal profit value from part (c). - 34600

(e) Using new technology, the total production can now be up to 200 units (i.e. less or equal to 200 units). Use the values from part (c) and part (d) to approximate the new maximal profit.

(f) Calculate the true new maximal profit for part (e) and compare with its approximate value you obtained. By what percentage is the true maximal profit different from the approximate value?

I need an explanation for (e) and (f)!!!!! Thanks for your help!!!!!