Operations Management - Linear Programming Projects

Answer all questions. Metallica, a metal furniture firm, produces three types of office chairs from steel

Answer all questions.

Metallica, a metal furniture firm, produces three types of office chairs from steel and aluminum. The three types of chairs are Baron, Secretary, and Executive. Each chair must pass through the forming and assembly departments. The company wants to know the optimal number of each type of chair to produce in order to maximize their profit. The profit per unit for each type of chair, and resource requirements are given in the following linear programming (LP) formulation.

Let the optimal number of Baron chairs be X ₁ ,

Let the optimal number of Secretary chairs be X ₂

Let the optimal number of Executive chairs be X ₃

Maximize profit, Z = 4X ₁ + 8.5X ₂ + 8X ₃ (profit,$)

subject to;

0.5X ₁ + 1.5X ₂ + 1X ₃ $\le $ 450 (steel, lbs)

1X ₁ + 1X ₂ + 1X ₃ $\le $ 430 (aluminum, lbs)

1X ₁ + 0.1X ₂ + 0.2X ₃ $\le $ 80 (forming, hrs)

0.3X ₁ + 0.2X ₂ + 0.1X ₃ $\le $ 50 (assembly, hrs)

X ₁ ,X ₂ ,X ₃ $\ge $ 0

Using the computer solution output on the next page , answer the following questions.

What is the optimal daily production plan for Metallica? That is, how many Baron, Secretary, and Executive chairs each, Metallica should produce daily in order to maximize their profit.
What would the firm's optimal profit be?
Which Metallica resources are unused at the end of each day’s shift?
Would you support a 2-hour reduction in the amount of hours available in the assembly department? Why or why not?
Would you support a 5-lb increase in daily steel availability at a cost of $4.00 per lb.? Why or why not?
If the profit from each Baron chair changed from $4.00 to $10.00, would the company’s daily optimal production plan change? Explain.
Would you support asking an employee in the forming dept to work overtime for one hour each day at the total cost of $14 per hour? Why or why not?
Suppose that 4lbs of aluminum supplied on a given day are bad, what would the full impact of this on output and or profit?

2. For this transshipment problem, assume that there are two sources, three intermediate warehouses and two final destinations, and travel is only possible between the sources and the warehouses, and between the warehouses and all destinations. In addition, assume that no travel is possible between the sources, between the warehouses, and between destination points. Also, there is no direct travel from any of the sources to any of the final destinations. Let the source nodes be labeled as 1 and 2, the warehouses be labeled as nodes 3, 4 and 5, and the final destination points be labeled as nodes 6 and 7. If there are 800 and 500 units available at sources 1and 2 respectively, and the demands at destinations 6 and 7 are 750 and 600 units respectively, formulate a linear programming model of the problem that could be used to determine how the shipment should be made so as to minimize total cost? The shipping costs are shown in the table below.

To (Destination)

3 4 5 6 7