Sensitivity Analysis Question:

A company manufactures four different products: X₁, X₂, X₃ and X₄.

	Contribution per unit,
X1	15.00
X2	6.20
X3	21.00
X4	25.00

The resource requirements for producing one unit of each of the four products and the resource capacity available per week are:

	Labour time in the Assembly department, minutes	Labour time in the Packing department, minutes	Material B, kg
X1	20	2.0	1.2
X2	12	1.0	0.5
X3	20	2.0	1.5
X4	30	1.0	2
Total Capacity available	105,000	6,000	6,480

Required:

1. Provide an explanation of the meanings of each of the terms in the final Tableau below, where X_i is the number of units of each product (i=1,2,3,4) produced per week, and S_1, S₂ and S₃ are slack variables for the labour time in the Assembly department, the labour time in the Packing department and Material B, respectively.

Final Tableau

	X1	X2	X3	X4	S1	S2	S3	Solution
S1	4.80	6.00	0	0	1	2.00	-16.00	13,320
X3	1.12	0.60	1	0	0	0.80	-0.40	2,208
X4	-0.24	-0.20	0	1	0	-0.60	0.80	1,584
Z	2.52	1.40	0	0	0	1.80	11.60	85,968

(8 marks)

2. Using the Final Tableau above, investigate the impact on the production plan, the total contribution generated per week and on the labour time remaining of the following:

1. Production of 80 units of Product X₂ to satisfy an influential customer.

(2 marks)

2. Paying an overtime premium per hour of 28.00 in the Packing department for an additional 20 hours.

(2 marks)