At What Level Of Output Are Total Profit Maximized 545712

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 – .5P

where P is price. Total costs (including a “normal” return to the owners) of producing Q units per period are:
TC = 20,000 + 50Q + 3Q R3

a) Express total profits (π) in terms of Q.
b) At what level of output are total profit maximized? What price will be charged? What are total profits at this output level?
a) What model of market pricing has been assumed in this problem? Justify your answer.