Q1) The Warren & Smith Company manufactures commercial zippers of two kinds, kind X and kind Y. Its production department estimates that the profit function of the firm is                                          

Π = 6X² + 10Y² – XY + 30

(i) The manager of the firm would like to know the level of output of zipper X and Zipper Y at which the profit of the firm is maximized and the level of this maximum profit.  

(ii) The firm expects an order of both zippers that will require it to produce X+Y = 34 unit of both kinds of zippers (each unit may be a large number of zippers), and so the manager would also like to know how many of each type of zipper the firm must produce to maximize its profit, and what its maximum profit would be if it receives the order 

Q2) A firm's demand function is 

                                                            Q = 40 - 2P

and its total cost function is defined as 

TC = 100 + 2Q + 0.25 Q². 

•  Use these two functions to form the firm's profit function and then determine the level of output that yields the maximum profit. What is the level of profit at the optimum level of output?