OPRE 315: Homework 3 Please answer the following questions giving all details. Please include the computer output with your submission. Question 1 and 3: 1 Point each Question 2: 2 Points 1. The Charm City Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwichesham and cheese, grilled vegetables and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes, a grilled vegetables sandwich requires 0.4 minutes, and a chicken salad sandwich requires 0.60 minutes to make. The company has 960 available minutes each night for making the sandwiches. The profit for a ham and cheese sandwich is $0.40, the profit for a grilled vegetables sandwich is $0.35 and the profit for a chicken salad sandwich is $0.50. The total number of sandwiches must be less than or equal to 2000. The company can make only 500 or less of ham and cheese sandwiches. The company's management wants to know how many of each kind of sandwich it should make to maximize profit. Formulate a linear programming model for the above situation by determining (a) The decision variables. HC: How many ham and cheese sandwiches to make. GV: How many grilled vegetables sandwiches to make. CS: How many chicken salad sandwiches to make (b) Determine the objective function. What does it represent? Maximize profit Max= 0.40(HC) + 0.35(GV) + 0.50(CS) (c) Determine all the constraints. Briefly describe what each constraint represents. The total number of sandwiches must be less than or equal to 2000; HC + GV + CS <= 2000; Can make only 500 or less ham and cheese sandwiches; HC<= 500; Total time to make the sandwiches must be less than or equal to the available 960 minutes; 0.45(HC) + 0.40(GV) + 0.60(CS) <= 960; Hint: There are 3 variables and 3 constraints (in addition to the non-negativity constraints) for this problem. 2. Find the computer solution, including the sensitivity analysis (ranging) results, for Question 1 by using QM for Windows or Excel. Determine the optimal solution and optimal profit. Interpret the optimal solution and optimal profit. 1 From using the QM, I see that the optimal solution results in a profit of $826.25, obtained from making 500 ham and cheese sandwiches, 825 grilled vegetables sandwiches and 675 chicken salad sandwiches. 3. Answer the following questions by using the sensitivity analysis (ranging) results from Question 2. Do NOT solve the problem again by using any computer software. (a) If the profit from a ham and cheese sandwich increases from $0.4 to $0.5, will the optimal number the three kinds of sandwiches made change? Will the total profit change? If they change, what will be the new optimal solution and the new total profit? (b) If the profit from a grilled vegetables sandwich increases from $0.35 to $0.45, will the optimal number of the three kinds of sandwiches made change? Will the total profit change? (c) The company has an opportunity to acquire some extra minutes of sandwich making. What is the maximum price the company should pay for each minute of additional sandwich making time, and how many additional minutes of sandwich making should they acquire at that price? Notes: - Homework 3 is due by midnight Saturday, March 12th. - Each student must solve Homework 3 problems individually by himself/herself or within the team he/she is a member of. Please do not ask for help from anyone else to answer any questions in this homework. - Please include all details and steps performed to find your answers. Just writing the final answers will not get you full credit. - Please post your answers in the Assignments section of the course website. - A team can post their answers in the Assignments section of the course website by any one of the team members but the submission must contain names of all team members. A member whose name is missing from the assignment will not receive any credit. - A team submission will be graded based on the answers submitted by the team. If answer to one or more questions is missing because a member of the team did not do his/her part, then the team will not receive any credit for those questions. 2