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

pA =900?2x?2y, pB =1400?2x?4y

respectively, where the firm produces and sells x units ofcommodity 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) Show that the firms total profit is given by:

?(x,y)=?3x^2 ?10y^2 ?4xy+800x+1400y?17000.

(b) Assume ?(x, y) has a maximum point. Find, step by step, theproduction levels that maximize profit by solving the first-orderconditions. If you need to solve any system of linear equations,use Cramer’s rule and provide all calculation details.

(c) Due to technology constraints, the total production must berestricted to be exactly 60 units. Find, step by step, theproduction levels that now maximize profits – using the LagrangeMethod. If you need to solve any system of linear equations, useCramer’s rule and provide all calculation details. You may assumethat the optimal point exists in this case.

(d) Report the Lagrange multiplier value at the maximum pointand the maximal profit value from part (c). No explanation isneeded.

(e) Using new technology, the total production can now be up to200 units (i.e. less or equal to 200 units). Use the values frompart (c) and part (d) to approximate the new maximal profit.

(f) Calculate the true new maximal profit for part (e) andcompare with its approximate value you obtained. By what percentageis the true maximal profit different from the approximatevalue?

I only need answers for part(e) and (f)!!!!!! Thanks foryour help!!!!!