Modern Electronics sells two popular models of wireless headphones, model A and model B. The sales of these products are not independent of each other (in economics, we call these substitutable products because if the price of one increases, sales of the other will increase). The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model: (N) a equals 20 - 0.62Pa 0.30Pb (N) b equals 29 - 0.10Pa 0.60Pb A. Construct a mathematical model for the total revenue. B. What is the predicted revenue if PA = + 18 and PB = + 30? What if the prices are PA = + 25 and PB - + 50?

If a firm sells two goods as is the case here, where the firm is selling two models of cameras--A and B--the total revenue generated is the revenue generated from camera A plus the revenue generated from camera B. Here:

The revenue from camera A model = (Price of camera A) x (quantity sold of camera A) = PA x NA

The revenue from camera B model = (Price of camera B) x (quantity sold of camera B) = PB x NB

We've been given the following:

NA = 190 - 0.7PA + 0.35PB

NB = 300 + 0.07PA - 0.6PB

This is where:

PA = Price of camera model A

NA = Quantity sold of the camera model A

PB = Price of the camera model B

NB = Quantity sold of the camera model B

Here, since the goods are substitutes of each other, the quantity sold of one good is dependent on the price of that good and its substitute good.