The price p a book company charges for its most recent book is related to the demand q in weekly sales by the equation 100pq+q² = 5,000,000.
Suppose the price is set at $40, which would make the demand 1,000 copies per week.
a) Using implicit differentiation, compute the rate of change of demand with respect to price, and interpret the result. (Round the answer to two decimal places.)
b) Use the result of part (a) to compute the rate of change of revenue with respect to price. Should the price be raised or lowered to increase revenue?
