Suppose you are a marketing manager. Let Xt denote the market share of your firm at Day t. Today is Day 0 and your firm occupies 10% of the market (in other words, X0 = 0.1). Given Xt , we can predict Xt+1 using the following formula.

 

 Xt+1 = min(1, At ∗ √ 1 − Xt − 0.09 ∗ Xt + Xt)

 

 In the above formula, At is the marketing expenditure on Day t. As the marketing manager, you need to select one of the following marketing plans for the next 100 days.

 

Plan (a): At = √ 1 − Xt Plan (b): At = 0.3 √ 1 − Xt

 

create program to answer the following questions for Plan (a): 

 

(1) create two arrays. One array includes the market shares on Days 0, 1, . . . , 100. One array includes the marketing expenditures on Days 0, 1, . . . , 100. Print two arrays.

 

 (2) Suppose the revenue of occupying Xt market share is 0.15Xt . The net revenue is the revenue minus the marketing expenditure, that is, the net revenue is 0.15Xt − At . Generate a new array that includes net revenues on Days 0, 1, . . . , 100. Print the array. 

 

(3) Because of the inflation, 1 dollar on Day t equals 2.71828−0.01t dollar on Day 0. Converted all net revenues in the array to the value on Day 0 and display the total net revenue on Day 0. (4) Repeat (1), (2), and (3) for Plan (b). (5) Print which plan results in a higher total net revenue. You need to upload your .java source file on eLearning. Your code should be format appropriately. (Hint: in java, √ a is written as Math.sqrt(a). min(a, b) is written as Math.min(a, b))