An organic chemical C is produced by the reaction of chemicals A and B as shown by the following second order elementary reaction: A + B C.

The initial amount of A introduced is x, kg while the initial amount of B introduced is y kg.

A material balance shows that the weight in kg of C produced is given by the equation: z = 1.5(1.1xz+1.3yz-xy)1/2 .

Raw material cost for A is USD 20/kg and for B, it costs USD 10/kg with other costs USD 14 per kg of C.

The product C sells for PhP 100 per kg.

Find the optimum amounts of reactants A and B needed and the maximum profit obtainable per kg of product C.