The production functions of three different Firms utilizing L and K in producing goods A, B, and C are given below. The three firms face the same fixed price for labor (5/unit) and capital (10/unit)

A = KL²- L³;B = 10K^1.5L^0.5;C = K^0.5L^0.5

Assume an economy with 100 units of labor and capital must be completely distributed to Firms A and B. Recommendan efficient allocation of the two inputs between the two firms by solving and discussing the answer.