A company uses pipelines to transfer fuel to different departments in

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Sol:
The total of all B-C-D-E-F-G-H-I is 1400. So if requirement is to be fully met, 1400 should flow out of Source-A. This is part-2 of the question.

Each line has a cap of 700,

If we take line-2 : B+D+G = 120+240+200 = 560 and therefore, 140 is still available, which can be used for H or I.

If we take line-1 upto F : C+E+F = 150+180+170 = 500, and therefore, 200 is still available in line EH.

A total requirement of H+I is = 190 + 150 = 340.

H can use line EH to get 190 and pass on the surplus 10 on H-I, remaining 140 for I shall come from line-2.

Line E-H thus have 200 as the flow. This is part-1 of the question.

Total consumption=1400, Hence total flow out from A has to be 1400

As per max capacity of pipeline of 700, A splits 700 in each fuel, now calculating the movement of oil,
Flow in CE is 700-150;
Flow in EF =170, consumption in E is 180
we get FLOW of 200(550-170-180) in EH

Given that The maximum capacity of the pipeline is 700 liters.

If the entire requirement of all departments is met, then
200
liters of fuel flows in the pipeline EH, and
700
liters of fuel flows out from the main source A.

Here,

Sum of value at each node is = 1400, So, 1400 litres of fuels flow out of source A.

Now,
If 1400 liter flows out of A than 700 litres moves towards C and 700 litres towards B.

Now, (700 - 150) = 550 litres flows from C to E.

(550 - 180) = 370 litres remaining of which 170 litres flows towards E to F

and remaining 200 litres fuels flows from E to H.

A company uses pipelines to transfer fuel to different departments in the company. The flowchart above shows the movement of fuel from the main source A to different departments shown by the alphabets B to I. The fuel is transferred only once a day as per the combined requirement of the departments and the direction is shown by the arrow. The remaining fuel moves ahead only after meeting the requirement of a particular department. The maximum capacity of the pipeline is 700 liters.

For example, if 500 liters move from A to C, then 350 liters move from C to E after fulfilling the requirement at department C.

From each drop down menu, select the option that creates the most accurate statement based on the information given.

If the entire requirement of all departments is met, then 200 liters of fuel flows in the pipeline EH, and 1400 liters of fuel flows out from the main source A.

Fuel flowing out from the main source A = Sum of requirement of all departments = 1400 litres
Since maximum pipeline capacity is 700 litres, Fuel flowing in pipeline AC = Fuel flowing in pipeline AB = 700 litres
Remaining flows in different pipelines are shown in figure above.

Remember the condition that the maximum pipeline is 700. Additionally, the sum of all the values is 1400.
The condition say "If the entire requirement of all departments is met,"
So, The pipeline A->C should be 700 and the pipeline A-->B should be 700 too

Total A: 1400

A-->C: 700
C-->E: 550
E-->F: 170
E-->H: 200 -->This is the answer

A-->B: 700
B-->D: 240
B-->G: 340
G-->H: 140

Finally, H-->I: 150

Answers: 200 and 1400

A company uses pipelines to transfer fuel to different departments in the company. The flowchart above shows the movement of fuel from the main source A to different departments shown by the alphabets B to I. The fuel is transferred only once a day as per the combined requirement of the departments and the direction is shown by the arrow. The remaining fuel moves ahead only after meeting the requirement of a particular department. The maximum capacity of the pipeline is 700 liters.

For example, if 500 liters move from A to C, then 350 liters move from C to E after fulfilling the requirement at department C.

From each drop down menu, select the option that creates the most accurate statement based on the information given.

Ans --
If the entire requirement of all departments is met, then
-- [/b]1400 (Total Qty Reqd -> summ of all points -> 150+180+170120+240+200+190+150 -> 1400)[/b] liters of fuel flows in the pipeline EH,
and -- [/b]200 (image with workings given below)[/b] liters of fuel flows out from the main source A.

Total fuel flowing through AB = 240+120+200+x(h)=560+x(h)
Total fuel flowing through AC = 150+180+170+y(h)=500+y(h)
Since maximum 700 l can flow through one pipe and total required fuel is 1400 therefore 700l flow through each pipe.
Hence Fuel flowing through EH=200

Total Fuel at A = sum of fuel at each station = 240+120+200+150+180+170+190+150 = 1400

All the liters add up to 1400.

B+D+G+H=750, but the maximum capacity of the pipeline is 700 liters, so at least 50 must come from E to H.
As we also need to provide fuel to I (150), then 150+50=200 liters flow in the pipeline EH.

So the total fuel that flows from A to C is C+E+F+200=700, which is also its maximum capacity.

Fuel from A to B = X1
Fuel from A to C = X2
Fuel from G to H = Y1 = X1 - 560
Fuel from E to H = Y2 = X2 - 500



total fuel required at H = 190+150 = 340

fuel at H after consumption by all departments before H
= Y1 + Y2 = (X1 - 560) + (X2 - 500) = 340
X1 + X2 = 1400 --> total fuel at source

X1 <= 700 --> X1 - 560 <= 140 --> Y1 <= 140
Similarly,
X2 <= 700 -> X2 - 500 <= 200 --> Y2 <=200

also Y1 = 340 - Y2
for Y2 = 200 , Y1 = 140 --> correct
for Y2 = 190 , Y1 = 150 ---> not allowed

Answer - Fuel from E to H = 200
Total Fuel at source = 1400

We can easily trace each pipeline, starting with B and C, to determine the amount of fuel that must flow only through that line. for the line starting at B, we get 560 and for C we get 500. This leaves capacity of 140 in line B and 200 in line C. Looking at H & I, 140+200 = 190+150, so we know we will use the full capacity of both lines to fill them. This gives 200 for E-H, and 1400 total.

This one was a bit of a beast!!! I went with 200, 1400.

I worked backwards from this one. First, we know the PIPELINE max is 700 but not the overall max. summing the fuel depot capacities, we get 1400, so know that flows into A...

The max pipeline tells us that 700 flowed out of A into each pipeline since the 1400 has to be evenly split. To see how much flowed into EH, I decided I first saw H and I needed 340 total - perfect, that's the answer! Or so I thought - then i realized we needed to consider the flow from the other side so I tracked that.

If AB had 700 to start, we subtract B, D, and G's capacities so we have: 700 - 120 - 240 - 200 = 700 - 560 = 140 so we get 140 from the B side flowing into H and we need 340 total, so we subtract 140 from 340 to get 200 total fuel needed from EH!

Let's say EH = x
GH = y

=> x+y = 190+150 = 340

=> CE = 350+x => AC = 500+x = 700 => x = 200

=> BG = 200+y => AB = 560+y =700 => y = 140

Fuel flowing out from A = 1400

If the entire requirement of all departments is met, then 200 liters of fuel flows in the pipeline EH
ie
700-240-120-200-190-150

and 1400 liters of fuel flows out from the main source A.
ie
240+120+15+180+170+200+190+150

Let's use the greedy approach to solve this problem.

On the top arches:
Node F requires 170L which only Node E can fulfil.
Node E requires minimum of 170L + 180L = 350L which only Node C can fulfil.
Node C requires minimum of 350L + 150L = 500L which only Node A can fulfil.
> Node A needs to send a minimum of 500L towards Node C and can additionally send 200L (As 700 is max).

On the bottom arches:
Node I requires 150L which only Node H can fulfil.
Node H requires minimum of 150L + 190L = 340L which Node E and Node G can fulfil.
Node G requires minimum of 200L (consider it sends 0 to Node H for time being) which only Node B can fulfil.
Node D requires minimum of 240L which Node E and Node B can fulfil.
Node B requires minimum of 240L + 200 L + 120L = 560L which only Node A can fulfil.
> Node A needs to send a minimum of 560L towards Node B and can additionally send 140L (As 700 is max).

Note: We still haven't satisfied 340L required at Node H.
Now, the maximum quantity that node A can supply still is 140L + 200L which is equal to 340L what Node H requires.
=> Node H will get 140L from bottom arch ie. via Node G
=> Node H will get 200L from top arch ie. via Node E. (Answer to first option).

Also, Node A is pumping out full 700+700 = 1400L (Answer to second option).

IMO answer is 200 L, 1400 L

Since the requirement of all department is to be met

Total fuel from two main pipelines to be = 150+180+170+190+120+240+200+150 = 1400L

Since each line can have max flow of 700L . So flow in AC line will be 700L and flow in AB line will be 700L. So flow in EH line will be 700-150-180-170 =200L

If the entire requirement of all departments is met, then liters of fuel flows in the pipeline EH= 200 liter . We do back calculation since all departments are getting filled
H and I need 340, Let EH =x , then GH=340-x and BG= 540-x, BD=240, AB=900-x
EF=170, CE=350+x, AC=500+x
Max that can be in a pipe is 700 thus x= 700-500=200


liters of fuel flows out from the main source A= Sum of fuel required by each department = 1400 liters