S09-HW Soln-SupC - Supplement C Linear Programming Homework...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Supplement C: Linear Programming Homework Problems Probett Problem #1: Solve these problems using simultaneous equations to determine the optimal values of the decision variables and the objective function. a. Maximize Z = 4x1 + 3x2 Subject to: Material: 6x1 + 4x2 <= 48 lb Labor: 4x1 + 8x2 <= 80 hr x1, x2 >= 0 b. Maximize Z = 6A + 3B Subject to: Material: 20A + 6B <= 600 lb Machinery: 25A + 20B <= 1000 hr A, B >= 0 Probett Problem #2: An appliance manufacturer produces two models of microwave ovens: H and W, Both models require fabrication and assembly work; each H uses four hours of fabrication and two hours of assembly, and each W uses two hours of fabrication and six hours of assembly. There are 600 fabrication hours available this week and 480 hours of assembly. Each H contributes $40 to profits, and each W contributes $30 to profits. What quantities of H and W will maximize profit? What is the maximum profit? Probett Problem #3: Solve each of these problems using Excel and obtain the optimal values of the decision variables and the objective function. Print the Excel “Answer Report”. a. Maximize Z = 4x1 + 2x2 + 5x3 Subject to: 1x1 + 2x2 + 1x3 <= 25 1x1 + 4x2 + 2x3 <= 40 3x1 + 3x2 + 1x3 <= 30 x1, x2, x3 >= 0 b. Max Z = 10x1 + 6x2 + 3x3 Subject to 1x1 + 1x2 + 2x3 <= 25 2x1 + 1x2 + 4x3 <= 40 1x1 + 2x2 + 3x3 <= 40 x1, x2, x3 >= 0 Probett Problem #4: The Erlanger Manufacturing Company makes two products. The profit estimates are $25 for each unit of product 1 sold and $30 for each unit of product 2 sold. The labor-hour 515dda97bdfc2ec15881744255b09f996c6a8c96.doc 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Supplement C: Linear Programming Homework Problems requirements for the products in the three production departments are shown in the following table. Product Department 1 2 A 1.50 3.00 B 2.00 1.00 C 0.25 0.25 The departments’ production supervisors estimate that the following number of labor- hours will be available during the next month: 450 hours in department A, 350 hours in department B, and 50 hours in department C. a. Develop a linear programming model to maximize profits. b. Find the optimal solution. How much of each product should be produced, and what is the projected profit? c. What are the scheduled production time and slack time in each department? Probett Problem #5: M&D Chemicals produces two products sold as raw materials to companies manufacturing bath soaps, laundry detergents, and other soap products. Based on an analysis of current inventory levels and potential demand for the coming month, M&D’s managers have specified that the total production of products 1 and 2 combined must be at least 350 gallons. Also, a major customer’s order for 125 gallons of product 1 must be satisfied. Product 1 requires two hours of processing time per gallon, and product 2 requires one hour; 600 hours of processing time are available in the coming month.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern