HitPhone Inc. is considering whether to introduce a new model of smart phone called model S18. The profitability of model S18 will depend on the following factors:a. Fixed cost of developing model S18: Fixed cost is normally distributed with mean $7.5 billion and standard deviation $1 billion. The fixed cost incurs only once in year 1.b. Sales: Assume that year 1 sales will be normally distributed with mean 2,500,000 and standard deviation 450,000. Sales are expected to increase for 2, 3, 4, 5 years with the average percentage increase during those years following a discrete random variable having 15% with probability 0.2, 20% with probability 0.5, and 25% with probability 0.3. Then sales are expected to increase for 6, 7, 8, 9, 10 years with the average percentage increase during those years following a discrete random variable having -5% with probability 0.3, 1% with probability 0.4, and 5% with probability 0.3. (Note that the realizations of increments for different years may be different).c. Price: Assume year 1 price is $1200. The sales price will be increased by 5% with probability 0.4 and 6% with probability 0.6 each year (Note that the realizations of increments for different years may be different).d. Variable cost per phone: variable cost is equally likely to be $300, $400, $500, or $600 during year 1, i.e, the probability of each outcome is 1/4. The variable cost is expected to increase with the average percentage increase during those years following a discrete random variable have 4% with probability 0.5 and 5% with probability 0.5 (Note that the realizations of increments for different years may be different).

Questions: 1) Simulate 500 trials and estimate the mean and standard deviation of the net profit for the first 10 years of sales and development for the model S18. What is the probability that the total profit exceeding 5 billion?2) Suppose that if the net total profit from year 1 to year 5 is below 14 billion, then the company must make a loan from the bank with interest rate 5% per year to bring the sum of the net profit and the loan back to 14 billion at year 5. The company repays the loan and the associated interests in year 10. Simulate 500 trials and estimate the mean and standard deviation of the net profit for the first 10 years of sales and development for the model S18, also estimate the average loan amount.3) Suppose that the mean of sales of year 1 sales changed to 3,000,000, 4,000,000, 5,000,000, 6,000,000, what are the corresponding average profits for the 10 years? Please use the two-way data table. (Suppose that all other problem data remains unchanged and simulate 500 trials for each case)