Determine the root of the following equation using the Newton-Raphson method with an initial guess of x = 1. Show two iterations. Hint if then, and if then.

Solve the following model using the simple method. Show all the steps for each iteration and clearly state the values for each of the variables (objective value, decisions variables, and slack variable) for each iteration. Be sure to clearly show the final answer to the problem. Maximize z = 2x1 + 1x2 subject to: 1x1 + 1x2 ? 12 10x1 + 1x2 ? 30 and x1, x2 ? 0 3. You have decided to enter the candy business. You are considering producing two types of candies: slugger candy and easy out candy, both of which consist solely of sugar, nuts, and chocolate. At present, you have in stock 100 oz of sugar, 20 oz of nuts, and 30 oz of chocolate. The mixture used to make easy out candy must contain at least 20% nuts. The mixture used to make slugger candy must contain at least 10% nuts and 10% chocolate. Each ounce of easy out candy can be sold for 25 cents, and each ounce of slugger candy for 20 cents. Formulate an lp that will enable you to maximize your revenue from candy sales. Formulate a linear programming model for this problem by:

Listing and labeling all of the decision variables.