The zinger company manufactures and sells a line of sewing machines

the Zinger company manufactures and sells a line of sewing machines. demand per period (Q) for a particular model is given by the following relationship:
Q=400-0.5P, where P is price.
Total cost (including a "normal" return to the owners) of producing Q units per period are:
TC= 20000+50Q+3Q2

a) Express total profits in terms of Q
b) at what level of output are total profits maximized? what price will be charged? what are total profits at this output?