Ms. Jennifer Lawrence, Amazon.com's brand manager of Kindle Fire (which costs $50 to produce and is sold directly to consumers through Amazon.com) has estimated the Scan*Pro demand model for her brand based on historical sales data and it looks as shown below.

DEMAND = [exp (10.0315)] * PRICE -2.5631 * AD 0.1051 * ADPP1 0.0635 * ADPP2 0.0376,

where DEMAND stands for the demand for Kindle Fire in a given week (in units sold), PRICE stands for the price of Kindle Fire that week (in $), AD stands for the advertising spending on Kindle Fire that week (in $), ADPP1 stands for the advertising spending on Kindle Fire during the previous week (in $), and ADPP2 stands for the advertising spending on Kindle Fire two weeks prior to the current week (in $).

1. Use the Optimal Mark-up Rule to calculate the optimal price for Kindle Fire.

2. Use the Dorfman-Steiner relationship to calculate what percentage of sales must be optimally spent on advertising for the Kindle Fire.

3. Write down the equation representing weekly brand profit for the Kindle Fire. Use Solver to maximize this profit by changing PRICE and AD (assuming that ADPP1 = ADPP2 = $1). Report the resulting optimal values of PRICE and AD. How does this optimal price compare to that calculated in question 1? Why? How does this optimal advertising compare to what is implied by the optimal A/S ratio that you calculated in question 2? Why?

Suppose Ms. Jennifer Lawrence is now managing two brands, Kindle Fire and Kindle Fire HD (which cost $50 and $75 to produce, respectively). She re-estimates the Scan*Pro demand model separately for her two brands, based on historical sales data, and the two Scan*Pro models look as shown below.

DEMAND1 = [exp (9.2365)] * PRICE1 -2.5811 * PRICE2 0.1509 * AD1 0.1050 * AD1PP1 0.0633 * AD1PP2 0.0375,
DEMAND2 = [exp (7.2739)] * PRICE1 0.0865 * PRICE2 -2.0542 * AD2 0.1152 * AD2PP1 0.0573 * AD2PP2 0.0289,

where DEMAND1 and DEMAND2 stand for the demands for Kindle Fire and Kindle Fire HD, respectively, in a given week (in units sold), PRICE1 and PRICE2 stand for the prices of Kindle Fire and Kindle Fire HD, respectively, that week (in $), AD1 and AD2 stand for the advertising spending on Kindle Fire and Kindle Fire HD, respectively, that week (in $), AD1PP1 and AD2PP1 stand for the advertising spending on Kindle Fire and Kindle Fire HD, respectively, during the previous week (in $), and AD1PP2 and AD2PP2 stand for the advertising spending on Kindle Fire and Kindle Fire HD, respectively two weeks prior to the current week (in $). (Note: These Scan*Pro specifications reveal that each brand's demand is impacted by the other brand's price, but not by the other brand's advertising spending).

4. Write down the equation representing weekly product portfolio profit (i.e., weekly brand profit from the Kindle Fire plus weekly brand profit from the Kindle Fire HD) for Ms. Jennifer Lawrence. Use Solver to maximize this profit by changing PRICE1, PRICE2, AD1 and AD2 (assuming that AD1PP1 = AD2PP1 = AD1PP2 = AD2PP2 = $1). How does the optimal price of Kindle Fire, i.e., PRICE1, compare to that calculated in question 3? Why? How does the optimal advertising for the Kindle Fire, i.e., AD1, compare to that calculated in question 3? Why?