Question

The Camera Shop sells two popular models of digital SLR cameras (Camera A Price: 200, Camera A Price: 300). The sales of these products are not independent of each other, but rather if the price of one increase, the sales of the other will increase. In economics, these two camera models are called substitutable products. The store wishes to establish a pricing policy o maximize revenue rom these products. A study of price and sales data shows the fol in relationships etween he quan ·sīd and prices (P) of each model: NA 195-0.5PA+0.35PB Ns-300 +0.06PA-0.5Ps Construct a model for the total revenue and implement it on a spreadsheet. Develop two-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. Max profit occurs at Camera A price of $ Max profit occurs at Camera B price of $

Answer 1

Total Revenue from selling camera A at price $P_A$ and camera B at $P_B$ is

$\begin{align*} \text{Total Revenue}&=\text{Revenue from A}+\text{Revenue from B}\\ &=\text{Quantity Sold of A}\times \text{Price of A}+\text{Quantity Sold of B}\times \text{Price of B}\\ &=N_A\times P_A+N_B\times P_B\\ &=(195-0.5P_A+0.35P_B)\times P_A+(300+0.06P_A-0.5P_B)\times P_B \end{align*}$

First let us create the model for total revenue as below

Get these values

Next we create the following 2 way data table

extend the rows and columns to get a value of 500 for each.

Now select the data in cells B9:AB35, set up data-->what if analysis-->data table as below

get the following

From the above we can see that the maximum total revenue is $105,768 and it occurs at camera A price of $380 and camera B price of $460

ans: Max Revenue (not necessarily profit) occurs at Camera A price of $380

Max Revenue (not necessarily profit) occurs at Camera B price of $460