) Quality Products (E.A) Ltd manufactures two products A and B. Experimental sales programs have shown that when the price per unit of A is p, the number x of units of A that will be sold is given by X = 12 - P/3, called demand function for A. The demand function for B is Y = 8 - Q/5, where q is the price for each unit of B. In addition, the cost C of manufacturing and selling x units of A and y units of B is given by C = X² + 2XY + 3Y²

Determine the prices to set per unit of A and B in order to maximize profit and the maximum profit.