Industrial Engineering Miscellaneous Difficult Questions and Answers | Page - 2

Industrial Engineering Miscellaneous

A project has four activities P, O, H and S as shown below.

The normal cost of the project is Rs. 10,000/- and the overhead cost is Rs 200/- per day. If the project duration has to be crashed down to 9 days, the total cost (in Rupees) of the project is_________ .

1. 11;500
1. 12,510
1. 12,500
1. 12,490

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Critical path ⇒ 1 – 2 – 3 – 4
⇒ 5 + 4 + 1 + 2 = 12 days
For 12 days :-
10,000 + 12 (200) = 12400
For 9 days :-
= 10,000 + 9 (200) + (400 + 300)
= 12,500

Correct Option: C

Critical path ⇒ 1 – 2 – 3 – 4
⇒ 5 + 4 + 1 + 2 = 12 days
For 12 days :-
10,000 + 12 (200) = 12400
For 9 days :-
= 10,000 + 9 (200) + (400 + 300)
= 12,500

If duration of activity f is changed to 10 days, then the critical path for the project is

1. Critical path remains the same and the total duration to complete the project changes to 19 days.
1. Critical path and the total duration to complete the project remains the same.
1. Critical path changes but the total duration tocomplete the project remains the same.
1. Critical path changes and the total duration to complete the project changes to 17 days.

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If duration of activity F has changed to 10 days, critical path remains the same and project duration will increase to 19 days.

Correct Option: A

If duration of activity F has changed to 10 days, critical path remains the same and project duration will increase to 19 days.

For the linear programming problem:
Maximize z = 3x₁ + 2x₂
Subject to –2x₁ + 3x₂ ≤ 9
x₁ – 5x₂ ≥ – 20
x₁, x₂ ≥ 0
The above problem has

1. unbounded solution
1. infeasible solution
1. alternative optimum solution
1. degenerate solution

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Maximize Z = 3X₁ + 2X₂
Subject to
– 2X₁ + 3X₂ ≤ 9
X₁ – 5X₂ ≥ 20
X₁, X₂ ≥ 0

Correct Option: C

Maximize Z = 3X₁ + 2X₂
Subject to
– 2X₁ + 3X₂ ≤ 9
X₁ – 5X₂ ≥ 20
X₁, X₂ ≥ 0

Consider an objective function Z(x₁, x₂) = 3x₁ + 9x₂ and the constraints
x₁ + x₂ ≤ 8
x₁ + 2x₂ ≤ 4
x₁ ≥ 0, x₂ ≥ 0
The maximum value of the objective function is __________.

1. 10
1. 18
1. 20
1. 14

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Z = 3x₁ + 4x₂
x₁ + x₂ ≤ 8
x₁ + 2x₁ ≤ 4
x₁, x₁ ≥ 0

At point A:
z = 3 (4) +9 (0) = 12
At point B:
z = 3 (0) + 9 (2) = 18

Correct Option: B

Z = 3x₁ + 4x₂
x₁ + x₂ ≤ 8
x₁ + 2x₁ ≤ 4
x₁, x₁ ≥ 0

At point A:
z = 3 (4) +9 (0) = 12
At point B:
z = 3 (0) + 9 (2) = 18

A linear programming problem is shown below:
Maximise 3x + 7y
Subjeot to 3x + 7y ≤ 10
4x + 6y ≤ 8
x, y ≥ 0

1. an unbounded objective function
1. exactly one optimal solution
1. exactly two optimal solution
1. infinitely many optimal solution

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z = 3x + 7y
Constraints 3x + 7y ≤ 10
4x + 6y < 8; x, y > 0
Corresponding equations
3x + 7y = 10; 4x + 6y = 8

A (0, 4/3) z = 9.23
B (2, 0) z = 6
Thus, exactly one optimal solution.
Hence, the correct option is (b).

Correct Option: B

z = 3x + 7y
Constraints 3x + 7y ≤ 10
4x + 6y < 8; x, y > 0
Corresponding equations
3x + 7y = 10; 4x + 6y = 8

A (0, 4/3) z = 9.23
B (2, 0) z = 6
Thus, exactly one optimal solution.
Hence, the correct option is (b).