MGT 397, Management Science Chapter 3 Assignment Spring 2022

ANSWER ALL QUESTIONS ( Show All Work)

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 = 48X₁ + 45X₂ + 40X₃

subject to;

X₃ 10 (market demand) (Constraint 1)

4X₁ + 3X₂ + 4X₃ 800 (steel, lbs) (Constraint 2)

2X₁ + 6X₂ + 2X₃ 820 (aluminum, lbs) (Constraint 3)

3X₁ + 2X₂ + X₃ 580 ( leather, square yards) (Constraint 4)

X₁ + 8X₂ + 2X₃ 720 (forging, hrs) (Constraint 5)

2X₁ + 4X₂ + 2X₃ 585 (assembly, hrs) (Constraint 6)

X₁,X₂,X₃ 0

Input the linear programming formulation above in QM for Windows 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. Screen shot of your computer solution output is worth 5 points.

a. 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.

b. What would Zeniths optimal daily profit be?

c. 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, indicating unused amounts if any.

d. The company can hire additional part-time employee that would increase the hours available in the assembly department by 4 hours daily, at the cost of $5.15 per hour. Should she be hired? Explain. Give reason for your answer.