Better Buy is having a sale this weekend on digital cameras. Its two most popular models are on sale but their sales are not independent. If the price of one increases, the sales of the other increases. In economics this is referred to as substitutable products. The store wants to establish a pricing policy to maximize revenue for these two cameras. A study of price and sales data shows the following relationships between the quantities sold (Q) and the price (P) of each model:
Q1 = 195 – 0.60P1 + 0.25P2
Q2 = 301 + 0.08P1 - 0.50P2
a. Construct a model for the total revenue and implement it on a spreadsheet.
b. Develop a 2-way data table to estimate the optimal prices for each product in order to maximize the total revenue. Vary each price from $250 to $500 in increments of $10.