Question

The Radio Shop sells two popular models of portable sport radios: 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 increase, sales of the other will increase). The store wishes to establish a pricing policy to maximize revenue from the products. A study of price and sales data shows the following relationships between the quantity sold (N) and prices (P) of each model (i.e. PA → Price of model A, NA  → Number of model A sold, etc.):

NA = 20 – 0.62PA + 0.30PB

NB = 29 + 0.10PA – 0.60PB

1. Construct a spreadsheet model for the total revenue.
2. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue.
3. Use Solver to find the optimal prices.
4. Write a Python code which takes the value of PA and PB and calculates the total revenue. Copy a screenshot of your code in your solution or share the link of your code.

Answer 1

1)

Here the Cost is basically referring to the amount incurred by the company for attaining a finished product. Thus the raw material used for manufacturing the finished product is termed as production cost. Similarly, in order to implement a system in the organization, various costs are associated with it which depends on the level of the system and the company.

2)

a.

It is needed to construct the model for the total revenue. Revenue refers to the money which is actually received by the company during a specific period that involves deduction and discount.

It can be expressed by the formula given below:

3)

b.

Predicted revenue refers to the money a particular company is estimated to generate underlying a particular time periods. The forecast is usually made for annual, quarterly, and monthly periods. The revenue is projected by the company by making use of internal knowledge and a combination of research.

It is required to find the predicted revenue if is $18 and is $30. It can be computed with the appropriate formula in the spreadsheet given below:

The corresponding values are:

Hence, it is ascertained that the total revenue accounts for  $705.12

4)

Now, if the price changes where is $25 and is $50. It can be computed with the appropriate formula in the spreadsheet given below:

The corresponding values are:

Hence, it is ascertained that the total revenue accounts for $562.50