Linear Programming For every problem below, include the full linear program on your answer sheet. Remember to clearly state the decision variables, objective function, and the constraints. Including ONLY the Excel sheet is NOT enough. Note: The value of some decision variables should be integer values, but this constraint can (and should) be ignored for this problem set. Make sure to include your solution as-is and do NOT round your solutions to integer numbers. Problem 1: As the manager of a newly opened restaurant, you are trying to decide the best way to allocate the available raw material to the four Friday night specials. The table below contains the information on the food and the amounts required for each item. Taco | Cheese Burger Sloppy Joes 0.3 0.25 0. 10 0 Food Ground Beef (lbs.) Cheese (lbs.) Beans (lbs.) Lettuce (lbs.) Tomato (lbs.) Buns Taco Shells Available 100 lbs. 50 lbs. 50 lbs. 15 lbs. 50 lbs. 80 buns 80 shells 0 One other fact relevant to your decision is the market demand and selling price. Cheese Burger 75 $2.25 Demand Selling Price Sloppy Joes 60 $2.00 Taco 100 $1.75 Chili 5 5 $2.50 Part A. Formulate an LP problem that maximizes the total revenue. Include the full linear program on your answer sheet, and clearly state the decision variables, objective function, and the constraints. You do not have to solve for the solution in this part, just show the mathematical formulation. Part B (Excel). Build a linear programming spreadsheet model in Excel, and solve it using Solver. Based on your solution, what is the best mix of the Friday night specials? And what is the maximum revenue? Problem 2: You are the check-in supervisor of an airline. Agents are scheduled for five consecutive days of work followed by the next two off. This schedule is repeated every week. Thus, each agent has the same day off each week. The number of agents needed each day is given in the table below, this number varies daily since, for example, more people travel on Friday than Wednesday. Agents Needed Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday 28 38 Part A. Formulate a linear program that will minimize the total number of workers needed to meet the daily demands. Include the full linear program in your work, and clearly state the decision variables, objective function, and the constraints. You do not have to solve for the solution in this part, just show the mathematical formulation. Part B. There is a new corporate policy that no new workers are allowed to start on Tuesday. State how your LP formulation in Part A will change. Part C. Suppose that we need to ensure that at least 60% of the workers have Friday off. State how your LP formulation in Part A will change. Part D (Excel). Build a linear programming spreadsheet model in Excel, and solve it using Solver. Include both policies from Part B and Part C. Error checking hint: The optimal objective function value is an integer whose digits sum to 14