Hello if you could help me with this I would highly appreciate this!

Question

When a bookstore sells a book at the price of P=12 per copy (in pounds), the monthly demand is Qd=700. When the book is sold at the price P=9, the monthly demand is Qd= 1000. Assuming linear dependence of Qd on P in the form Qd=adP+bD,

1. Determine aD and bD

2. Determine the revenue R(P) of the bookstore as function of the price P

3. Find the maximum possible revenue Ropt and the corresponding price Popt.

Answer 1

Q=aP + b

700=12a+b

1000=9a+b

By elimination a=-100 and b=1900

i.e. Q=1900-100P

R=1900P-100P²

dR/dP=1900-200P=0

P_max=9.5

You can now find the max revenue.