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. The Pizza Man offers plain, meat, vegetable, and supreme pizzas. Each variety has its own requirement of sauce, cheese, dough, and toppings (in ounces as shown in the table), and each has its own selling price. The Pizza Man would like to determine what the right combination of pizzas to make (using its existing stock of ingredients) to maximize revenue from its sales. a) (3 pts) What are the decision variables in this problem? b) (3 pts) State the objective (as a function of the inputs specified in the problem and the decision variables defined in (a)). c) (5 pts) What are the constraints in this problem? Write an algebraic expression for each. d) (10 pts) Solve the problem using Excel solver. - Please submit your Solver model and output (Answer report). - What is the maximum sales revenue? - What mix of pizzas should be made to achieve this sales revenue (interpret the optimal solution)? (e) (4 pts) Which ingredients are economically scarce (i.e., they are limiting our profits)? Explain your answer. A chemical company manufactures three chemicals: A,B, and C. These chemicals are produced via two production processes: 1 and 2 . Running process 1 for an hour costs $400 and yields 300 units of A,100 units of B, and 100 units of C. Running process 2 for an hour costs $100 and yields 100 units of A and 100 units of B. To meet customer demands, at least 1000 units of A,500 units of B, and 300 units of C must be produced daily. The company would like to determine a daily production plan that minimizes the cost of meeting the daily demand. a) (3 pts) What are the decision variables in this problem? b) ( 3 pts) State the objective (as a function of the inputs specified in the problem and the decision variables defined in (a)). c) (5 pts) What are the constraints in this problem? Write an algebraic expression for each. d) (10 pts) Solve the problem using Excel solver. - Please submit your Solver model and output (Answer report). - What is the minimum cost? - What daily production plan should be made to achieve this cost (interpret the optimal solution)? e) (4 pts) Suppose that the hourly processing cost for process 2 increases by $50. How will the optimal value change? Explain your answer using the results from part (d)
