## Pro Statistics

- A manufacturer is preparing to set the price on a new action game. Demand is thought to depend on the price and is represented by the model: D = 2, 000 3. 5P

The accounting department estimates that the total costs can be represented by:

C = 5, 000 + 4. 1D

a. Develop a model for the total profit and implement it on a spreadsheet.

b. Develop a one-way data table to evaluate profit as a function of price (choose a price range that is reasonable and appropriate).

c. Use Solver to find the price that maximizes profit.

- 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 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:

NA = 20 0. 62PA + 0. 30PB

NB = 29 + 0. 10PA 0. 60PB

a. Construct a model for the total revenue and implement it on a spreadsheet.

b. Develop a two-way data table to estimate the optimal prices for each product in order to maximize the total revenue.

- Each worksheet in the Excel file LineFit Data contains a set of data that describes a functional relationship

between the dependent variable y and the independent variable x. Construct a line chart of each data set, and

use the Add Trendline tool to determine the best-fitting functions to model these data sets. - Develop a spreadsheet model to determine how much a person or a couple can afford to spend on a house.

Lender guidelines suggest that the allowable monthly housing expenditure should be no more than 28% of monthly gross income. From this, you must subtract total nonmortgage housing expenses, which would include insurance and property taxes, and any other additional expenses. This defines the affordable monthly mortgage payment. In addition, guidelines also suggest that total affordable monthly debt payments, including housing expenses, should not exceed 36% of gross monthly income. This is calculated by subtracting total nonmortgage housing expenses and any other installment debt, such as car loans, student loans, credit card debt, and so on, from 36% of total monthly gross income. The smaller of the affordable monthly mortgage payment and the total affordable monthly debt payments is the affordable monthly mortgage. To calculate the maximum that can be borrowed, find the monthly payment per $1, 000 mortgage based on the current interest rate and duration of the loan. Divide the affordable monthly mortgage amount by this monthly payment to find the affordable mortgage. Assuming a 20% downpayment, the maximum price of a house would be the affordable mortgage divided by 0. 8.

### Use the following data to test your model: total

monthly gross income = $6, 500; nonmortgage housing expenses = $350; monthly installment debt = $500;

monthly payment per $1, 000 mortgage = $7. 258.

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