# Industrial Engineering

 Question 1
Which one of the options given represents the feasible region of the linear programming model:
\begin{aligned} Maximize\;\; 45X_1&+60X_2 \\ X_1&\leq 45 \\ X_2&\leq 50 \\ 10X_1+10X_2& \geq 600 \\ 25X_1+5X_2&\leq 750 \end{aligned} A Region P B Region Q C Region R D Region S
GATE ME 2023      Linear Programming
Question 1 Explanation:
\begin{aligned} x_1&=45 &...(i)\\ x_2&= 50&...(ii)\\ 10x_1+10x_2&=600 \\ or\; x_1+x_2&=60&...(iii) \\ 25x_1+5x_2&=750 \\ or\; 5x_1+x_2&=150&...(iv) \\ \end{aligned}
By drawing the curve we get 3 values of $x_1$ and $x_2$ as (10, 50), (20, 50), (22.5, 37.5)
So, $Z_{max}=45x_1+60x_2$ for (10,50)
$Z_{max}=450+3000=4450$
for (20,50)
$Z_{max}=45\times 20+50 \times 60=3900$
for (22.5, 37.5)
$Z_{max}=45\times 22.5+60 \times 37.5=3262.5$
So, $Z_{max}=3900\; for \; (x_1,x_2)=(20,50)$
 Question 2
With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? A Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost. B Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost. C Curve P1: Production cost, Curve P2: Holding cost, Curve P3: Total cost, and Curve P4: Setup cost. D Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.
GATE ME 2023      Inventory Control
Question 2 Explanation: Question 3
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
 A 3 and 3, respectively B $\sqrt{3}$ and $\sqrt{3}$ , respectively C 0.015 and 0.015, respectively D 3 and 9, respectively
GATE ME 2023      Production Planning and Control
Question 3 Explanation:
P = 0.015
n = 200
mean $=\lambda =np= 200 \times 0.015 = 3$
variance $=\sigma ^2=\lambda =3$
 Question 4
A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is __________ weeks (in integer).
$\begin{array}{|c|c|c|c|c|} \hline \text{Activity} & \text{Optimistic time (week)} & \text{Most likely time (week)} &\text{Pessimistic time (week)} &\text{Immediatepredecessor(s)} \\ \hline A& 4 & 5 &6 & None\\ \hline B& 1& 3 & 5 & A\\ \hline C& 1& 2 & 3 & A\\ \hline D& 2& 4 & 6 & C\\ \hline E& 3& 4 & 5 &B,D \\ \hline \end{array}$
 A 12 B 15 C 16 D 18
GATE ME 2022 SET-2      PERT and CPM
Question 4 Explanation:
$\begin{array}{|c|c|} \hline \text{Activity}& t_e=\frac{t_0+4t_m+t_p}{6}\\ \hline A&5\\ \hline B&3\\ \hline C&2\\ \hline D&4\\ \hline E&4 \\ \hline \end{array}$ $\begin{array}{|c|c|} \hline \text{Path}& \text{Duration}\\ \hline 1-2-4-5(A-B-E)&12\\ \hline 1-2-3-4-5 (A-C-D-E)&15\\ \hline \end{array}$
Expected completion time of the project = critical path duration = 15 weeks
 Question 5
A manufacturing unit produces two products P1 and P2. For each piece of P1 an P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is Rs __________.
$\begin{array}{|c|c|c|c|c|} \hline &\text{M1 } &\text{M2}&\text{M3}&\text{Profit per piece (Rs.)} \\ \hline P1 & 2 &2 &0&150\\ \hline P2 & 3& 1&2&100\\ \hline \text{Maximum quantity available per day}& 70& 50&40\\ \hline \end{array}$
 A 5000 B 4000 C 3000 D 6000
GATE ME 2022 SET-2      Linear Programming
Question 5 Explanation:
Let,
$x_1=$ No. of units of product $P_1$
$x_2=$ No. of units of product $P_2$
Max, $Z=150x_1+100x_2$
\begin{aligned} s.t.\;\; 2x_1+3x_2 &\leq 70 \\ 2x_1+3x_2&\leq 50 \\ 2x_2 &\leq 40 \\ x_1\geq 0, x_2&\geq 0 \end{aligned}

Point B: Intersection of

\begin{aligned} 2x_1+3x_2 &\leq 70 \\ 2x_2 &\leq 40 \\ x_2=20, x_1&=5 \end{aligned}

Point C: Intersection of
\begin{aligned} 2x_1+3x_2 &\leq 70 \\ 2x_1+x_2 &\leq 50 \\ \text{By sloving }2x_2 &=20 \\ \Rightarrow x_2=10, x_1&=20 \end{aligned} \begin{aligned} Z_{max}&=150x_1+100x_2\\ Z|_{A(0,20)}&=150(0)+100(20)=2000\\ Z|_{B(5,20)}&=150(5)+100(20)=2750\\ Z|_{C(20,10)}&=150(20)+100(10)=4000\\ Z|_{D(25,0)}&=150(25)+100(0)=3750\\ \Rightarrow x_1&=20,x_2=10\\ Z_{max}&=4000 \end{aligned}

There are 5 questions to complete.

### 3 thoughts on “Industrial Engineering”

1. Hello,

I believe the answer to question 8 is option D (CNC Milling Machines). Kindly make the changes accordingly.

• 2. 