questions 4-8 please thank you

MAT 11805 Project #2 Due November 21, 2022 In preparing a recipe you must decide what ingredients and how much of each ingredient you will use. In these health-conscious days, you may also want to consider the amount of certain nutrients in your recipe. You may even be interested in minimizing some quantities (like calories or fat) or maximizing others (like carbohydrates or protein). Linear programming techniques can help you to do this. For example, consider making a very simple trial mix from dry-roasted, unsalted peanuts and seedless raisins. The table below lists the amounts of various dietary quantities for these ingredients. The amounts are given per serving of the ingredient. Suppose that you want to make at most 6 cups of trail mix for a day hike. You don't want either ingredient to dominate the mixture, so you want the amount of raisins to be at least 1/2 of the amount of the peanuts and the amount of peanuts to be at least 1/2 of the amount of the raisins. You want entire amount of trail mix you make to have fewer than 4000 calories, and you want to maximize the amount of carbohydrates in the mix. 1. Let x be the number of cups of peanuts you will use, let y be the number of cups of raisins you will use, and let c be the amount of carbohydrates in the mix. Find the object function. 2. What constrains must be placed on the object function? 3. Graph the feasible region for this problem. 4. Find the number of cups of peanuts and raisins that maximize the amount of the carbohydrates in the mix. 5. How many grams of carbohydrates are in a cup of the final mix? How many calories? 6. Under all the constraints given above, what recipe for trail mix will maximize the amount of protein in the mix? How many grams of proteins are in a cup of this mix? How many calories? 7. Suppose you decide to eat at least 3 cups of the trial mix. Keeping all constrains given before, what recipe for trail mix will minimize the amount of fat in the mix? 8. How many grams of carbohydrates are in this mix? 9. How many grams of proteins are in this mix? 10. Which of the three trail mixes would you use? Why? 1. In part 3 you also need to find all corner points and label them. 2. For part 6 of the project, you should use the same feasible region as in part 3, but different object function: p (number of grams of proteins) in terms of x and y. You want maximize this function. 3. For part 7, you should use all constrains given before plus a new constrain determined by "you decide to eat at least 3 cups of the trial mix". So you have a feasible region which is different from part 3 and part 6 . You should graph this feasible region as well. Your object function for this part is f (number of grams of fat) in terms of x and y. You want minimize this function