A rm produces two products, A and B. The inverse demand functions are respectively, pg =6002m2y and p3 = 12002343:, which are indeed prices ofA and B per unit, where the rmproduces and sells 3 units of product A and 3: units of product B. Its costs are given by 0,4 = 5000 +100m+m2 and 03 = 0000 +6y2. (a) Show that the rm's total prot is given by: vr(:r,y) = -3m2 my2 4mg + 500m + 12001,: 14000. (b) Assume that (3, 3:) given by (a] has a maximum point. Find, step by step, the production levels (i.e. values of m and 1;] that maximise the prot by solving the rst-order conditions (If you need to solve any system of linear equations, use Cramer's rule and provide all calcula- tion details). [cl Due to technology constraints, the total production must be restricted to be exactly 55 units. Find, step by step, the production levels that now maximise the prot using the Lagrange Method. If you need to solve any system of linear equations, use Cramer's rule and provide all calculation details. You may assume that the optimal point exists in this case. (d) Report the Lagrange multiplier value at the maximum point; and the maximal prot value from part (c). No explanaon is needed. (e) Using new technology, the total production can now be up to 120 units (is. less than or equal to 129 units). Use the values from [c] and (d) to approximate the new maximal prot. (f) Calculate the true new maximal prot for part [c] and compare with its approximate value you obtained. By what percentage is the true maximal prot different from the approximate value