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
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.
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
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.
|Due By (Pacific Time)||04/24/2014 08:00 pm|
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