Linear Programming - Feasibility and Multiple optimal solution

An organization produces paints of two qualities A and B. Profit on A and B are given as Rs 500/ litre and Rs. 800/ litre respectively. These paints are made using three important Chemicals - L, M and N. Their requirements in Paint A are given as 30, 40 and 25 units per litre respectively. Corresponding numbers for Paint B are 50, 30 and 20. These chemicals are available in 1500, 1200 and 1000 units per day. The decision involved is related to quantity of paint A and paint B to be produced per day.

a) Give two examples of feasible solutions and explain why they are so.    

b) Give one example for which Chemicals M and N are available in sufficient quantities but Chemical L is short and explain why it is so.     

c) Change the profit value of paint B so that there are multiple optimal solutions with quantity of paint A to be produced being more than 15 litres/day.                  

And the solution is available at 

https://youtu.be/-lWG-v76EDc

Project Management

The work breakdown structure of a market research project is given below:  

Activity	Immediate predecessors	Activity time in days
A	-	20
B	-	15
C	-	25
D	A	10
E	B	20
F	C	18
G	D	8
H	A, E	12
I	A, E	10
J	C	14
K	G, H	25
L	F, I	22
M	J	30

a) Draw the activity-on-arrow network diagram and find the project completion time.   

b) What would be the project completion time if the activity time of K is reduced by 5 days? Don’t draw the network diagram again while solving this part of the question. 

The answer is available at
https://youtu.be/TdgSTM3UYso

        

Time series data and exponential smoothing forecasting

You are using exponential smoothing method to forecast the number of claims in health insurance.

a) How much weightage is given to actual claim data of 6^th month behind the forecast month? Assume the value of smoothing factor other than 0 and 1 while answering this question. 

    

b) Give two examples of time series data and one example of such data that is not time series. 

The answer is available at

https://drive.google.com/file/d/1xBFEe5D0VxbNvVjZsEDF7z9P5rqR834O/view?usp=sharing