Lp Formulation, Simulation

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MGMT 2012- Introduction to Quantitative MethodsGraded Assignment One

Students should note that this assignment should submitted in two files: Excel for Question 1 A and Word for the other questions.

Question 1 A
The Eastern Caribbean Central Bank has estimated that the outflow of US$ (foreign currency) to purchase motorcars is putting a terrible strain on the exchange rate. The Governments subsequently entered in negotiations with Nissan Motors of Japan, with the view to establishing an assembly plant in the OECS. Nissan conducted a feasibility study and concluded that if the deal were to go through then four plants would be needed. The following cost and requirements table was obtained:

PLANT

COST (US$)

LABOUR

RAW MATERIAL

1 (St Kitts/Nevis)

7,500

2

3

2 (Antigua)

5,000

3

4

3 (Grenada)

4,500

4

5

4 (Belize)

5,500

5

6

The costs given are to produce a car at each plant, respectively. Nissan must produce exactly 1,000 cars. At least 300 must be produced at plant 3. No more than 500 must be produced at plant 1. Labour hours available are at most 3,300, while raw material availability does not exceed 4000. Formulate an LP using the template given and solve in Excel to enable Nissan Motors to minimize the cost of production 20 marks (15 marks to formulate and 5 marks to solve in excel)

.

Question 1B

The Southfork Feed Company makes a feed mix from four ingredients oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix:







At least 30% of the mix must be soybeans.
At least 20% of the mix must be the vitamin supplement.
The ratio of corn to oats cannot exceed 2 to 1.
The amount of oats cannot exceed the amount of soybeans.
The mix must be at least 500 pounds.

A pound of oats costs $0.50; a pound of corn, $1.20; a pound of soybeans, $0.60; and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix in order to minimize cost. a. Formulate a linear programming model for this problem (Do not solve in excel).

18 marks for constraints and 2 marks for objective function (20 marks)

Question 2
Stop Fast brake makes brake shoes for motors at three locations in St Vincent, St Lucia and Dominica. These are identified as plant 1, plant 2, and plant 3 respectively. Each plant has sufficient capacity to produce 750 brake shoes per week. Labour (excluding cost), raw material and production costs required to build a brake are show in table below. Stop fast has 525 workers each paid 12.5 per hour worked; each can work up to 40 hours per week. Currently the firm has 9,400 units of raw materials in stock. Every week, at least 1400 brake shoes must be produced.

PLANT

COST (EC)

LABOUR

RAW MATERIAL

1 (St Vincent)

50

20 hrs

5 units

2 (St. Lucia)

80

16hrs

8 units

3 (Dominica)

100

10 hrs

7 units

Refer to the formulation below and output to answer the following questions.

Let Pj = number of brake shoes
produced at plant j; j = 1,…, 3
Min 300 P1 + 280 P2 + 225 P3

-

Decision
variables

Cost of production

Subject to:
P1 + P2 + P3

≥1400

Production requirement

P1

≤ 750

capacity to be produced

≤ 750

capacity to be produced

≤ 750

capacity to be produced

20 P1 + 16 P2 + 10 P3

≤ 21000

labour constraint

5P1 + 8 P2 + 7 P3

≤ 9400

raw material

P2
P3

Pj ≥ 0 for all j [Non-negativity]

Questions

a.
b.
c.
d.
e.

What is the optimal solution, in words? (2 marks).
Is there alternative optima? Explain! (1 mark).
Is the problem degenerate? Explain! (2 marks).
In the slack column, there is a symbol ???. What should this value be? (2 marks). The labour constraint has a shadow price...
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