Name: 2. (10 points) True or False. Please indicate whether each of the followin
ID: 3064873 • Letter: N
Question
Name: 2. (10 points) True or False. Please indicate whether each of the following statements is true or false (no explanation needed). 1) The optimal solution (or one of the optimal solutions) of a linear programming problem, if one exists, must be at an extreme point of the feasible region. 2) Increasing the right hand side (a scalar) of a constraint of a linear programming problem might decrease the optimal objective function valuc 3) Delay of an activity on the critical path of a project will delay the project 4) A shortest path problem should be solved to find the least expensive way to crash activities of a project to shorten the project duration The following screenshot shows a correct setup in the Excel Solver dialogue box for the LP problem in Question 1 (given that the formulas in the cells are all set up correctly). 5) C DEF x1 x2 By Changing Variable Cel 5812 5C12 2 D.V. o 4 O.F Change 6 Constraints LHS RHS Reset A -3Explanation / Answer
Answer to the question#1)
Feasible solutions are generally all the solutions that satisfy the given constraints. There can be infinite feasible solutions. It can be a complete region made of lines of constraints on a graph.
This feasible solution area may have some vertices, it is at these vertices one can expect either the objective to be maixmum or the minimum. Thus we hope to get the optimum solution at these extreme values of the feasible solution
Thus this statement is true
.
Answer to question# 2)
Increasing the right hand side of the constraints increases the area of feasible solutions and shifts them to the ight of the number line, this pulls the optiomal solution also to the right side of the number line and thus the optimal solution value also increases.
Hence this statement is False
.
Answer to question# 3)
A delay in one acticity on the critical path of the project, actually helps to reduce the idle time or the slack time. This ultimately doesnot affect the project time at all.
Thus the answer to this statement is false.
.
Answer to question# 4)
in the method of crashing the duration of the project is reduced byt crashing the leat expensive activities first
Yes, this statement is true
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