A firm is the only producer of two goods, X and Y. the demand equations for X and Y are given by ...

A firm is the only producer of two goods, X and Y. the demand equations for X and Y are given by:
 

x = 600 - pX – pY --- (1)
y = 450 - 1/2pX – pY --- (2)
 

where x and y are the quantities of X and Y demanded (respectively) and pX and pY are (respectively) the prices of X and Y. the firm's joint total cost function (that is, the cost of producing x of X and y of Y) is x^2+3xy+y^2+100
 

find an expression in terms of x and y for the profit function. Determine the quantities x and y that maximize the profit, and find the corresponding prices pX,pY.