A regional beer distributor has $100,000 to spend on advertising in four markets, where each market responds differently to advertising. Based on observations of each market's response to several advertising initiatives, the distributor has estimated the sales response by fitting a power curve R = axb, where R represents sales revenue, and x represents advertising dollars, both measured in thousands. The estimated curves are described in the following table:

Market __________________ Sales Revenue

Domestic ........................... 100x0.4

Premium ............................ 80x0.5

Light .............................. 120x0.3

Microbrew ......................... 60x0.6

a. Determine how the advertising dollars should be allocated to the four markets so that the sales revenue for the distributor is maximized.

b. If the distributor had $1,000 of additional funds in the advertising budget, by how much could total revenue be increased?

c. If the distributor had $2,000 of additional funds in the advertising budget beyond the base case in part (a), by how much could total revenue be increased?

d. Construct a graph showing the optimal total revenue as a function of the advertising budget, for budget sizes in the range $50,000 to $150,000.