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GATE 2019: Industrial Engineering Quiz 1

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Question 1

Consider an objective function Maximize

and the constraints

The maximum value of the objective function is ______.

Question 2

A linear programming problem is shown below:
Maximize Z

Subject to

It has

Question 3

A furniture manufacturer produces chairs and tables. The woodworking department is capable of producing 200 chairs or 100 tables or any proportionate combinations of these per weeks. The weekly demand for chairs and tables is limited to 150 and 80 units respectively. The profit from a chair is Rs. 100 and that from a table is Rs. 300. The maximum profit is ________.

Question 4

Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ____________.

Question 5

consider the following statements
(1) Dual model give objective value of LPP of less number of decision variables and more no of constraints.
(2) Dual variables are always non negative.
(3) Dual of unique optimal is unique optimal.
(4) if RHS of given constraint is changed by 1 unit, corresponding change in object value is dual variable.

Question 6

One unit of product P₁ requires 3 kg of resource R₁ and 1 kg of resource R₂. One unit of product P₂ requires 2 kg of resource R₁ and 2 kg of resource R₂. The profits per unit by selling product P₁ and P₂ are Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource R₁ and 100 kg resource R₂.

The unit worth of resource R₂, i.e. dual price of resource R₂ in Rs. per kg is

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ESE & GATE ME Industrial Engineering

Nov 20ESE & GATE ME