Page 87 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Table 3.3: The Second Basis
Row 1: P + x – s = 357,000
1 2
Row 2: x + s – s = 2,000
1 1 2
Row 3: x + x +s = 8,000
1 2 2
Row 4: x +a = 6,500
1 1
Since there is no variable with a negative coefficient in Row 1, no further improvement in profit
is possible. But artificial variable a1 continues to exist in Row 4 and it is also basic variable. This
means that the optimum solution has not been reached. The problem has no solution because of
infeasibility.



Case Study Linear Programming & Technical Accounting

A company manufactures 2 products a 10 cu. Ft & 6 cu. ft. refrigerator. The demand
for the former has been estimated at 15,000 and for the later at 24,000.

The production process is broken down into 3 stages:
1. Shell production
2. Motor assembly
3. Refrigerator assembly

The production manager estimates that the shell production unit can through put up to
36,000 smaller refrigerators, but only half of this quantity of the 10 cu. ft. product. Similarly,
the motor assembly unit can through put 30,000 smaller motors or 80% of this quantity of
the other product. The assembly department has no restrictions as labour unskilled is
required. The accounting function has produced the standard cost breakdown as follows:
Standard Costs of Production
(in Dollars)
Items 10 cu. ft 6 cu. ft.
Direct materials 30 24
Direct labour 16 10
Variable overhead 14 11
Marginal cost 60 45
Selling price 90 65
Contribution 30 20

Fixed overhead charges are estimated as $ 4,00,000.
Traditional accounting would entail the manufacture of 15,000 of the 10 cu ft. refrigerators
before the shell production unit capacity is exceeded only 6,000 smaller refrigerator would
be manufactured. On the basis of direct labour, $3,20,000 of fixed overheads would be
attributed to 10 cu. ft. & 80,000 to the 6 cu. ft.
Contd...

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