A firm is the only supplier of two goods, X and Y , and the demand equations for these goods are x = 76-pX and y = 50-(1/2)pY , where pX and pY are the prices of X and Y , and where x and y are (respectively) the amounts of X and Y . The firm has a total joint cost function TC = 2x^2 + 2xy + 3y^2 + 10. Find an expression, in terms of x and y, for the firm's profit. Determine also the values of x and y that will maximise this profit.