Chapter 10: Operations ResearchMarch 13, 2024 Maven Leave a Comment Welcome to the Chapter 10: Operations Research 1. Given an L.P.P. maximize Z =$2x_{1}+3x_{2}$ subject to the constraints $x_{1}+x_{2}\leq 1$; $5x_{1}+5x_{2}\geq 0$; $x_{1}\geq 0, x_{2}\geq 0$ using graphical method, we observe No feasible solution unique optimum solution multiple optimum solution none of these None 2. Network problems have advantage in terms of project Scheduling Planning Controlling All the above None 3. The objective of network analysis is to Minimize total project cost Minimize total project duration Minimize production delays, interruption and conflicts All the above None 4. In critical path analysis, the word CPM mean Critical path method Crash project management Critical project management Critical path management None 5. In the context of network, which of the following is not correct A network is a graphical representation A project network cannot have multiple initial and final nodes An arrow diagram is essentially a closed network An arrow representing an activity may not have a length and shape None 6. The maximum value of the objective function Z=3x+5y to the constraints $x\geq 0$ $y\geq 0$ $2x+5y\leq 10$ is 6 15 25 31 None 7. In a network while numbering the events which one of the following statement is false? Event numbers should be unique. Event numbering should be carried out on a sequential basis from left to right. The initial event is numbered 0 or 1. The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow. None 8. In the given graph the coordinates of M1 are $x_{1}=5; x_{2}=30$ $x_{1}=20; x_{2}=16$ $x_{1}=10; x_{2}=20$ $x_{1}=20; x_{2}=30$ None 9. The minimum value of the objective function Z = x + 3y subject to the constraints $2x + y \leq 20$, $x + 2y \leq 20$, x>0 and y>0 is 10 20 0 5 None 10. The critical path of the following network is 1 – 2 – 4 – 5 1– 3– 5 1 – 2 – 3 – 5 1 – 2 – 3 – 4 – 5 None 11. In constructing the network which one of the following statement is false? Each activity is represented by one and only one arrow. (i.e.) only one activity can connect any two nodes. Two activities can be identified by the same head and tail events. Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity. Arrows should not cross each other. None 12. Maximize: $z=3x_{1}+4x_{2}$ subject to $2x_{1}+x_{2}\leq 40$; $2x_{1}+5x_{2}\leq 180$; $x_{1}, x_{1}\geq 0$. In the LPP, which one of the following is feasible corner point? $x_{1}=18$; $x_{2}=24$ $x_{1}=15$; $x_{2}=30$ $x_{1}=2.5$ $x_{2}=35$ $x_{1}=20$; $x_{2}=19$ None 13. One of the conditions for the activity (i, j) to lie on the critical path is $E_{j}-E_{i}=L_{j}-L_{i}=t_{ij}$ $E_{i}-E_{j}=L_{j}-L_{i}=t_{ij}$ $E_{j}-E_{i}=L_{i}-L_{j}=t_{ij}$ $E_{j}-E_{i}=L_{j}-L_{i}\neq t_{ij}$ None 14. A solution which maximizes or minimizes the given LPP is called a solution a feasible solution an optimal solution none of these None 15. Which of the following is not correct? Objective that we aim to maximize or minimize Constraints that we need to specify Decision variables that we need to determine Decision variables are to be unrestricted. None Time's upRelated Posts:Chapter 1: Introduction to Micro EconomicsChapter 2. Consumption AnalysisChapter 3: Production AnalysisChapter 4: Cost and Revenue Analysis
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