Sensitivity Analysis Question:

A company manufactures four variants of the same product (Product X), and in the final part of the manufacturing process there are Assembly, Polishing and Packing operations. For each variant the time required for these operations is shown below (in minutes per unit) as is the profit per unit sold.

Variant Assembly Polishing Packing Profit (£)
X1 2 3 2 1.50
X2 4 2 3 2.50
X3 3 3 2 3.00
X4 7 4 5 4.50
Given the current state of the labour force, the company estimate that, each year, they have 100,000 minutes of Assembly time, 50,800 minutes of Polishing time and 60,000 minutes of Packing time available.

A solution to the linear programme is given below, where S1, S2 and S3 are slack variables for the labour time for the Assembly, Polishing and Packing operations, respectively.

Final Tableau

X1

X2

X3

X4

S1

S2

S3

Solution

S1

-1.0

0

0

0.2

1

-0.2

-1.2

17,840

X3

1.0

0

1

0.4

0

0.6

-0.4

6,480

X2

0.0

1

0

1.4

0

-0.4

0.6

15,680

Z

1.5

0

0

0.2

0

0.8

0.3

58,640

Required
1. Provide an explanation of the meanings of each of the terms in the final Tableau above.

(6 marks)

2. What if 200 units of the product X1 and 500 units of the product X4 should be produced to satisfy an influential customer? What will be the new production plan and the total contribution generated per year? Also, state the impact of this on the resources remaining.

(6 marks)

Total = 12 marks