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Quantitative Business Methods

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Submitted By Sandery
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DERY CYRIL DOMEYELLE EBA LEVEL: 300
QUANTITATIVE BUSINESS METHODS
ASSIGNMENT

(A)

Let x = number of units of product X y = number of units of product Y z = number of units of product Z

Maximize 20x + 18y + 16z (Objective function)

Subject to 5x + 3y + 6z ≤ 3,000 (Machine hours constraint) 2x + 5y + 3z ≤ 2,500 (Labour hours constraint)

8x + 10y + 3z ≤ 10,000 (Materials constraint)

Changing the inequalities into equalities and adding a slack variable

Maximize 20x + 18y + 16z (Objective function)

Subject to 5x + 3y + 6z + S1 = 3,000 2x + 5y + 3z + S2 = 2,500

8x + 10y + 3z + S3 = 10,000

Initial Simplex Tableau

Solution Variables Products

X Y Z
Slack Variables

S1 S2 S3
S1 5 3 6 1 0 0 3,000
S2 2 5 3 0 1 0 2,500
S3 8 10 3 0 0 0 10,000
Z 20 18 16 0 0 0 0
(B)

Initial Simplex Tableau

Solution Variables Products

X Y Z
Slack Variables

S₁ S₂ S₃
S₁ 5 3 6 1 0 0 3,000
S₂ 2 5 3 0 1 0 2,500
S₃ 8 10 3 0 0 0 10,000
Z 20 18 16 0 0 0 0

3,000/5 = 600

2,500/2 = 1,250

10,000/8 = 1,250

Therefore, the pivot element in row S₁ and column X is 5.

Dividing the non-zero elements in row S₁ by 5 to make the pivot element 1:

S₁ 5/5 3/5

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