Homework: Management Science
Task
Zenith, a small metal furniture firm, produces three types of office chairs from steel, aluminum, and leather. The three types of chairs are Baron, Secretary, and Executive. Let X1, X2, and X3 respectively be the optimal number of Baron, Secretary, and Executive chairs to be produced daily. Profit for each Baron chair is $48.0, for each Secretary chair, it is $45.0, and for each Executive chair, it is $40.0. Each chair must pass through the forging and assembly departments. The manager produced the following linear programming formulation for the problem to determine the optimal solution. Input the model in a software (QM for Windows) you downloaded and solve it. Then, using your computer output, answer the questions below.
Maximize (profit, $) Z = 43X1 + 40X2 + 38X3
subject to;
X3≥11(market demand) (Constraint 1)
4X1 + 3X2 + 4X3≤800 (steel, lbs) (Constraint 2)
2X1 + 6X2 + 2X3 ≤750 (aluminum, lbs) (Constraint 3)
3X1 + 2X2 + X3 ≤ 570 ( leather, square yards) (Constraint 4)
X1 + 8X2 + 2X3≤720 (forging, hrs) (Constraint 5)
2X1 + 4X2 + 2X3≤680 (assembly, hrs) (Constraint 6)
X1,X2,X3≥ 0
Input the linear programming formulation above in QM for Windows or Excel QM software you downloaded, and solve it. Save your computer solution output in a file. Using the computer solution output, answer the following questions (a to g), Type out your answers, save as a Word document and submit it together with the saved screen shot of your computer solution output.
o What is the optimal daily production quantity for each type of chair at Zenith? (That is, how many of each type of chair should Zenith optimally produce daily?) They would be the values of X1, X2, and X3 in the optimal solution.
o What would Zenith's optimal daily profit be?
o Will Zenith use all the available quantities of each of its resources (steel, aluminum, leather, forging hours, and assembly hours) to their limits each day? Be specific for each resource, by indicating unused amounts of each resource if any.
o Some peopleapplied to Zenith to work in the assembly department. Should the company currently hire them? Give reason for your answer.
o Zenith's General Manager has been approached by a friend whose company would like to use some hours daily in either the forgingor assemblydepartment or both. Should Zenith sell some hoursin any or both departments to the other firm? If so, specify the number of hours Zenithcan sell in each department to this other firm?Give reasons for your answers.
o Suppose that 20 pounds of aluminum supplied on any given day are defective and could not be used, would itchange the optimal daily production quantity for each specific type of chair at Zenith? Give reason for your answer.
Format your homework according to the following formatting requirements:
o The answer should be typed, using Times New Roman font (size 12), double spaced, with one-inch margins on all sides.
o The response also includes a cover page containing the title of the homework, the student's name, the course title, and the date. The cover page is not included in the required page length.
o Also include a reference page. The Citations and references must follow APA format. The reference page is not included in the required page length.