The demand function for a manufacturer's product is p = f(q)= 800 - 2q,where p is the price (in dollars)per unit when q units are demanded (per week).Find the level of production that maximizes the manufacturer's total revenue.
A) 100
B) 125
C) 150
D) 175
E) 200

Question

Quizplus · Accepted Answer

The total revenue (R) is given by the product of price (p) and quantity (q), so R = pq. Substituting the demand function into this equation gives R = (800 - 2q)q = 800q - 2q^2. To maximize revenue, we take the derivative of R with respect to q, set it to zero, and solve for q. dR/dq = 800 - 4q = 0. Solving for q gives q = 200.

The Demand Function for a Manufacturer's Product Is P =