# Determine an appropriate advertising policy.

i attached an example of algebraic model , please go through the questions attached and create a similar model
1- please build algbraic model ( mathematical model )
Continuing Problem 6, suppose the company is selling in the
United States, the United Kingdom, and Japan. Assume the unit
production cost is \$50, and the exchange rates are 1.22 (\$/£) and
0.00965 (\$/¥). Each country has its own constant elasticity demand
function. The parameters for the United States are 19,200,000 and
−2; the parameters for the United Kingdom are 10,933,620 and −2.2;
and the parameters for Japan are 15,003,380,400 and −1.9. The
company has a production capacity of 3000. Therefore, the company
can sell only as many units, in total, to all three countries as it
can produce.
2-please build algbraic model ( mathematical model )
In Example 7.5, we implied that each of the five observations
was from one period of time, such as a particular week. Suppose
instead that each is an average over several weeks. For example,
the 4.7 million exposures corresponding to one ad might really be
an average over 15 different weeks where one ad was shown in each
of these weeks. Similarly, the 90.3 million exposures corresponding
to 50 ads might really be an average over only three different
weeks where 50 ads were shown in each of these weeks. If the
observations are really averages over different numbers of weeks,
then simply summing the squared prediction errors doesn’t seem
appropriate. For example, it seems more appropriate that an average
over 15 weeks should get five times as much weight as an average
over only three weeks. Assume the five observations in the example
are really averages over 15 weeks, 10 weeks, 4 weeks, 3 weeks, and
1 week, respectively. Devise an appropriate fitting function, to
replace sum of squared errors or RMSE, and use it to find the best
fit.
J&J has given you \$12 million to spend on advertising Huggys diapers
during the next 12 months. At the beginning of January, Huggys has a
30% market share. During any month, 10% of the people who purchase
Huggys defect to brand X, and a fraction
of customers who usually buy brand X switch to Huggys, where a
is the amount spent on advertising in millions of dollars. For example,
if you spend \$4 million during a month, 40% of brand X’s customers
switch to Huggys. Your goal is to maximize J&J’s average market
share during the next 12 months, where the average is computed from each
month’s ending share. Determine an appropriate advertising policy. (Hint: Make sure you enter a nonzero trial value for each month’s advertising expense or Solver might give you an error message.)
63.
Consider
three investments. You are given the following means, standard
deviations, and correlations for the annual return on these three
investments. The means are 0.12, 0.15, and 0.20. The standard deviations
are 0.20, 0.30, and 0.40. The correlation between stocks 1 and 2 is
0.65, between stocks 1 and 3 is 0.75, and between stocks 2 and 3 is
0.41. You have \$10,000 to invest and can invest no more than half of
your money in any single stock. Determine the minimum-variance portfolio
that yields a mean annual return of at least 0.14.

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