Problem 1 - (75 points total) - Sabrina is the cafeteria manager for a school. She needs to minimize costs while maintaining the nutritional values. Each week, she buys the potatoes and green beans from a wholesaler. Potatoes cost $0.40 per pound, and green beans cost $1.00 per pound. Per state requirements each/dinner must contain at least 180 grams of protein, 80 milligrams of iron, and 1,050mg of vitamin C. Sabrina's research shows the following nutritional information about the three ingredients: A. Write the constraints and objective function equations in algebraic form which will give (if solved) the amount (weight) of potatoes and green beans Sabrina needs to purchase each week for the dish to minimize the total costs while meeting nutritional requirements. (20) B. Solve the problem to obtain the minimum cost given the constraints in Excel using linear programming (35). C. Add the constraint where the food needs to contain at least a two-to-one ratio in the weight of potatoes to green beans. What will be the minimum total cost now (show work on a different tab)? (10) D. Add another constraint to part C where the cost of green beans has increased by 20%. What is the optimum answer now