OPRE 315 Homework 2 1. A company manufactures two products: large fans and medium fans. Each large fan requires 3 hours of wiring and 2 hours of drilling. Each medium fan requires 2 hours of wiring and 1 hour of drilling. There are 480 hours of wiring time available and 280 hours of drilling time available. Each large fan yields a profit of $20. Each medium fan yields a profit of $15. The company wants to manufacture at least 20 large fans. The objective is to maximize total profit. (a) Formulate a linear programming model for this problem by defining the decision variables, objective function and all the constraints. What do they represent? (b) Find the optimal solution of this model by hand using the Corner Points graphical method. 2. Solve the following linear programming model graphically. In addition, write the problem in standard form and do a constraint analysis for the optimal solution. Show all details. Maximize 80x + 100y Subject to x + 2y < 20 4x + 4y < 60 x, y ≥ 0 3. The Charm City Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 55 milligrams of vitamin A and 30 milligrams of vitamin B while minimizing the total cost. An ounce of oats contributes 8.25 milligrams of vitamin A and 1.20 milligram of vitamin B, whereas an ounce of rice contributes 6.40 milligrams of vitamin A and 2.30 milligrams of vitamin B. An ounce of oats costs $0.14, and an ounce of rice costs $0.10. Formulate a linear programming model for the above situation by determining (a) The decision variables (b) Determine the objective function. What does it represent? (c) Determine all the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating. 4. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 5x + 10y Subject to -3x + 4y < 60 2x + 3y > 90 x, y > 0 1 Notes: - Homework 2 is due by midnight Sunday, September 23rd. - Each student must solve Homework 2 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. Also, do not share your answers with anyone except your team members. - Please include all details and steps performed to find your answers. Just writing the final answers will not get you full credit. - Some of the questions above require drawing graphs. Here is a list of options for you to include a graph in your answer. Draw the graph using MS Paint or CorelDraw or some other software. Copy the graph in a MS Word file and post the file on the course website in appropriate category. OR Draw the graph by hand on a paper, scan it or take a photo and post it with your answer. OR Describe the graph in words in your answer. - Please post your answers in assignments section of the course website. - A team should post their answers in the assignments section of the course website by any one of the team members. 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. - Please submit the homework answers in Microsoft Word or PDF format. Scans or photos of the answers are acceptable but they must be clear and legible. Other formats are not acceptable. 2
Purchase answer to see full attachment