The Pizza Man is a local shop that plans to make its sales this Saturday from its sidewalk tables during the town's holiday parade. On this occasion, the shop's owners know that customers will buy by the slice and any kind of pizza offered will sell completely. The Pizza Man offers plain, meat, vegetable, and supreme pizzas. Each variety has its own requirement of sauce, cheese, dough, and toppings (in ounces per pizza as shown in the table), and each has its own selling price (per pizza). Plain Meat Vegetable Supreme Available Dough 5 5 5 5 200 Sauce 3 3 3 3 90 Cheese 4 3 3 4 120 Meat 0 3 0 2 75 Vegetables 0 0 3 2 40 Price $8 $10 $12 $15 The Pizza Man would like to determine what is the right combination of pizzas to make (using its existing stock of ingredients) to maximize revenue from its sales. Write the Linear Program formulation for the above optimization problem. Make your formulation clear by defining the variables, constraints, objective function etc Solve it using Excel solver. Please attach your clearly annotated Solver model and output (including Answer and Sensitivity Report) as Exhibit What is the maximum sales revenue? What mix of pizzas should be made to achieve this sales revenue? Which ingredients are economically scarce (i.e., they are limiting to profits)? The following questions can be answered using the sensitivity report (the more tedious way to answer the question is by trial and error, running Solver after changing the data). Plain and Vegetable pizzas are not being produced in the optimal production plan. By how much should their selling price go up to make it economically sensible to produce plain and vegetable pizzas? The availability of sauce has gone down by 10 units. What will the new sales revenue be? The availability of sauce has gone down by 10 units. What will the new sales revenue be? Suppose you have an aquarium and your goal is to wisely feed the fish. You have several packets of fish food that weigh the following (in grams): Pk. # Wt. 1 2 2 5 3 17 4 31 5 16 6 21 7 14 8 27 9 19 10 18 11 15 You know that the fish requires at least 100 grams of food. At the same time, fish is a strange animal in the sense that if you feed it more food than it needs, then it will eat the extra food and may die. So, your goal is to pick a subset of these packets so that they weigh a total of at least 100 grams, but exceed the 100 grams limit by the least amount. a) Formulate this as an integer programming problem, and solve using Solver. Present the formulation together with a clearly annotated Solver model and output (Exhibit. b) Which packets would you include, and how many grams of food would you feed the fish? Feeding farm animals. Animals need: 14 units of nutrient A, 12 units of nutrient B, and 18 units of nutrient C. Two feed grains are available, X and Y. A bag of X has 2 units of A, 1 unit of B, and 1 unit of C. A bag of Y has 1 unit of A, 1 unit of B, and 3 units of C. A bag of X costs $2. A bag of Y costs $4. The farmer would like to minimize the cost of meeting the nutrient requirements. What are decision variables in this problem? What is the objective (as a function of the decision variables)? Enumerate all the constraints. Solve the optimization problem and describe the optimal solution. Generate the sensitivity report (attach as Exhibit Which of the constraints non-binding