# 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.

3- please create algebraic model

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.)

4- please create algbraic model

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.