Operations Research Answers

Given the constraints
A+B + C ≤ 24, B +C ≥ 8 and A ≥ 0, B ≥ 0, C ≥ 0.
Maximize 24-A-B - C
A: amount of time spent on school work
B: amount of time spent on fun
C: amount of time spent on pay work

How many types of failures are considered in replacement theory?

Execute the Job Assignment Problem and prove the solution

1.3 Minimize z = a + b + c
Subject to:
1. a - b - c ≤ 0
2. a + b + c ≥ 4
3. a + b - c = 2
4. a, b ≥ 0

How to solve the following linear program using simplex algorithm:

Minimizer z=a+b+c
Subject to 1.a-b-c lesser than or equal to 0
2.a+b+c greater than or equal to 4
3.a+b-c=2
4.a,b greater than or equal to 0

Solve the following linear program using simplex algorithm
Minimize z= a+b+c
Subject to: 1. a - b -c<=0
2. a + b + c>=4
3. a +b-c=2

Maximize Z = 2a + b – 3c + 5d
Subjected to;
a + 7b + 3c + 7d ≤ 46
3a – b + c +2d ≤ 8
2a + 3b – c + d ≤ 10
Where,
a, b, c, and d all are ≥ 0

A construction company wants to bid for a project which consists of four activities: A, B, C and D. Some of these activities can be completed in parallel, while some cannot start until others are completed. The time needed to complete each activity is normally distributed. You are the project planner of the company and is asked to estimate the completion time of the project so that when the company bids for it, they can avoid the tardiness penalty. Implement a simulation in Excel to determine the average completion time of this project. The completion time stated in current contract is 50 days, based on your estimation, what is the probability that the construction company can finish it within that time (i.e. the proportion of simulation trials that give a completion time less than or equal to 50 days)? In your solution, provide your estimates, and describe your simulation procedure in words.

State which of the following statements are true and which are false. Give reasons for
your answers with a short proof or a counter-example. (10)
i) The set of all convex combinations of a finite number of points 1 2 Xn X is not ,X ,...,
a convex set.
ii) If the pay-off matrix of a game is transformed, saddle point of the game if it exists,
changes.
iii) If a negative value appears in the solution values ) (XB
column of the simplex
method, then the basic solution is optimum.
iv) In an assignment problem, if a constant is added to each element of the matrix, the
optimal assignment does not change.
v) In an LPP, every feasible solution is optimal.