Industrial Engineering Miscellaneous
- Let Y1 and Y2 be the decision variables of the dual and v1 and v2 be the slack variables of the dual of the given linear programming problem. The optimum dual variables are
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The optimal dual variables are V1 & V2.
Correct Option: D
The optimal dual variables are V1 & V2.
- If an additional constraint X1 + X2 ≤ 5 is added, the optimal solution is
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Max z = x1 + x2
As feasibly region remains the same solution remains the same (4/3, 4/3).
Hence, the correct option is (b).Correct Option: B
Max z = x1 + x2
As feasibly region remains the same solution remains the same (4/3, 4/3).
Hence, the correct option is (b).
- A company has two factories S1, S2 and two warehouses D1, D2. The supplies from S1 and S2 are 50 and 40 units respectively. Warehouse D1 requires a minimum of 20 units and a maximum of 40 units. Warehouse D2 requires a minimum of 20 units and, over and above, it can take as much as can be supplied. A balanced transportation problem is to be formulated for the above situation. The number of supply points, the number of demand points, and the total supply (or total demand) in the balanced transportation problem respectively are
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Total no of supply point
⇒ m + n – 1
⇒ 2 + 2 – 1
⇒ 3
Total no of Demand point
= 4 (x11, x12, x21, x22)
Total supply = Total Demand
⇒ 90 unitsCorrect Option: C
Total no of supply point
⇒ m + n – 1
⇒ 2 + 2 – 1
⇒ 3
Total no of Demand point
= 4 (x11, x12, x21, x22)
Total supply = Total Demand
⇒ 90 units
- A component can be produced by any of the four processes, I, II, III and IV. Process I has fixed cost of Rs. 20 and variable cost of Rs. 3 per piece. Process II has a fixed cost of Rs. 50 and variable cost of Rs. 1 per piece. Process III has a fixed cost of Rs. 40.00 and variable cost of Rs. 2 per piece. Process IV has fixed cost of Rs. 10 and Variable cost Rs. 4 per piece. If company wishes to produce 100 pieces of the component, from economic point of view it should choose
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Total cost = Fixed Cost (FC) + Number of piece (n) × Variable Cost per piece (VC)
TC = FC + (n) x V.C
For I
TCI = 20+ (100) 3 = 320
For II
TCII = 50 + (100) 1 = 150
For III
TCIII = 40 + 100 (2) = 240
For IV
TCIV = 10 + 100 (4) = 410
So from economical point of view, one should chose process IICorrect Option: B
Total cost = Fixed Cost (FC) + Number of piece (n) × Variable Cost per piece (VC)
TC = FC + (n) x V.C
For I
TCI = 20+ (100) 3 = 320
For II
TCII = 50 + (100) 1 = 150
For III
TCIII = 40 + 100 (2) = 240
For IV
TCIV = 10 + 100 (4) = 410
So from economical point of view, one should chose process II
- A company has an annual demand of 1000 units, ordering cost of Rs. 100/ order and carrying cost of Rs. 100/unit-year. If the stockout costs are estimated to be nearly Rs. 400 each time the company runs out-of-stock, the safety stock justified by the carrying cost will be
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D = 1000 Units
CO = 100 Rs/order
Ch = 100/ unit/order
Cs = 400 each time
⇒ 50S* = Q * 
Ch 
= 50 100 CS + Ch 500
S* ⇒ 10
Softly Stock Justified by the carrying cost = Maximum Inventory level M = Q* – S* = 40Correct Option: C
D = 1000 Units
CO = 100 Rs/order
Ch = 100/ unit/order
Cs = 400 each time
⇒ 50S* = Q * Ch = 50 100 CS + Ch 500
S* ⇒ 10
Softly Stock Justified by the carrying cost = Maximum Inventory level M = Q* – S* = 40
