A company is trying to determine the optimal amount of money to invest in a new product. The company knows that the profit from the product will increase as the amount of money invested increases, but at a decreasing rate. The company wants to invest the optimal amount of money so that it maximizes its profit. However, the company also knows that there is a risk involved in investing in the new product. If the product fails, the company will lose all of the money that it invested. The company wants to balance the risk and reward of investing in the new product so that it maximizes its expected profit. If the company invests x dollars, its profit will be x 0.01x. The company has a budget of $100,000 to invest and the probability of the product failing is 0.2. How much should the company invest to maximize its profits? a) Solve the problem with one variable NLP method with using Cases. (pdf file) b) Solve the problem with one variable NLP method using MATLAB for calculations. Copy and paste your codes and solutions. (pdf file) c) Solve the problem with Newton's, Bisection, and Golden Section methods (You must show all three methods separately and do the calculations manually). (pdf file) d) Solve the problem with Newton's, Bisection, and Golden Section methods using EXCEL. (Excel file)