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GATE 2019:Industrial Engineering Rapid Revision Quiz

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Question 1

At a bike service station, bikes arrive according to Poisson’s distribution at a rate of 5 bikes per hour. The service time per bike is exponential at a rate of 5 bikes per hour. The service station can accommodate maximum 15 bikes. What is the probability that a bikes which comes and leaves without joining the queue?

Question 2

At a certain lathe machine, jobs arrive according to Poisson’s distribution at a rate of 24 jobs per hour. The average number of jobs that can be machined by the machine is 30 per hour. The probability of having exactly one job in the system and the probability that the machine is idle will be, respectively

Question 3

Match the correct pairs

Question 4

The earliest occurrence time for event '1' is 8 weeks and the latest occurrence time for event' I' is 26 weeks. The earliest occurrence time for event '2' is 32 weeks and the latest occurrence time for event '2' is 37 weeks. If the activity time is 11 weeks, then the total float will be:

Question 5

The forecast data for the months of april, may, june have 30%, 30%, and 40% weightage.
What will be the forecast for the month of july ? The demand for the months is 200, 145 & 190 respectively.

Question 6

A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is _______.

Question 7

In a forecasting model, at the end of period 13, the forecasted value for period 14 is 75. Actual value in the periods 14 to 16 are constant at 100. If the assumed simple exponential smoothing parameter is 0.5, then BIAS at the end of period 16 is

Question 8

For a single server system, the arrival rate is at an average of 8 minutes and the serving time in the system is 6 minutes. Find the average waiting time in the queue

Question 9

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 10

The demand for smartphone in a shop for last four months were 150 , 160,172, 176 . forecast for fourth month was 164 and forecast of fifth month using simple smoothening is equal to forecast using last three month moving average so find out mean absolute deviation at end of 4 month.

Question 11

Profit matrix is given which give profit obtained per unit for transportation from factories to market. now using VAM method for given unit profit matrix find total loss in transportation.

Question 12

Maximize Z = 3x₁ + 4x₂
Subject to x₁ + x₂ ≤ 1
-3x₁ + x₂ ≥ 3
x₁ ≥ 0, x₂ ≥ 0

Question 13

For a particular product, the following information is given:
Selling price per unit: Rs. 100
Variable cost per unit: Rs. 60
Fixed cost: Rs. 1000000
Due to inflation the variable cost have increased by 10% while fixed costs have increased by 5%. If the break even quantity is to remain constant, the percentage increase in sales price would be ___________.

Question 14

Standard machine tool and an automatic machine tool are being compared for the production of a component. Following data refers to the two machines.

The breakeven production batch size above which the automatic machine tool will be economical to use, will be _____ units.

Question 15

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______

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