Please use the following problem to help solve the bolded questions

6. Allocation. 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 tting a power curve R ax b , 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 100x^0.4

premium 80x^0.5

Light 120x^0.3

Microbrew 60x^0.6

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.

The parameters in the sales revenue response curves are now random but continue to follow the function given in the book: Ri=aixibi where R_i is the sales revenue generated in each market (in thousands of dollars), a_i is the first function parameter, x_i represents advertising dollars in each market (in thousands of dollars), and b_i is the second function parameter (the exponent). The function parameters, distributions, and distribution parameters are given in the table below:

Parameter:	a	a	a	b	b	b
Market	Distribution	Mean	Std. Dev.	Distribution	alpha	beta
Domestic	Normal	100	20	Beta	4	6
Premium	Normal	80	16	Beta	5	5
Light	Normal	120	24	Beta	3	7
Microbrew	Normal	60	12	Beta	6	4

(Note: draws from a normal distribution can be done in Excel using the function "=NORM.INV(RAND(),mean,standard_deviation)". Draws from a beta distribution can be done in Excel using the function "=BETA.INV(RAND(),alpha,beta)") The decisions (i.e., spending in each market) made were optimal without randomness and are shown below:

Market	Advertising Dollars Spent
Domestic	$15,718
Premium	$27,271
Light	$9,123
Microbrew	$47,888

A. what is the average simulated sales revenue

B. is the average simulated sales revenue higher or lower than the sales revenue when no uncertainty was present?

C. What is the probability that the uncertain sales revenue is greater than the sales revenue when no uncertainty was present? Note: answer should be between 0 and 1.