# Project #28692 - Stats HW

4.   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

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.

5.   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.

7.   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.

8.   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.

 Subject Computer Due By (Pacific Time) 04/24/2014 08:00 pm
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