Linear profit, graphs and equations.

[nihil404]

I have no clue how to interpret this problem and where to start to get my values to plot my graphs and get my x, y and etc values as there is too much going on.
Can someone shed some light of how to do this problem?

I am not sure if is this how I solve this:

How do I find that the HD subscriptions is twice as profitable?
And what the HD and SD customers existing customers have to do with the problem?

IO streams = 200
HD stream = 4 = x
SD stream = 1 = y
4x + 1y = 200

bandwidth cost

1.50 HD x
0.75 SD Y

1.5x + 0.75y = 100

Lease cost =80

HD = 1 x
SD = 0.75y
1x + 0.75y = 80Am I doing the correct calculations?

Thank you very much in advance for any help.You are to help a popular online VOD service maximise their profits by advising the company’s sale team on set ‘sales targets’ for “HD single screen” subscriptions and “SD single screen” subscriptions given that it is 2 times more profitable to sell SD single screen subscriptions than HD single screen ones.
It must also be noted that the company must honour its existing HD single screen (5) and SD single screen (10) subscribers.
Being an online company profits increase linearly in relation to the number of servers running. In this instance we will only look for the costings of running a single server. That being said, due to hardware limitations, a server can only stream 200 IO streams, where a HD stream consumes 4 IO streams and a SD stream only consumes 1 IO stream.
In terms of bandwidth cost, we have a simple contract that provides the first £100 worth (per month) of bandwidth free, after which the cost for bandwidth significantly increases such that users do not exceed this free £100 limit. It is to be noted that on average the bandwidth consumption (per month) of a typical HD subscription never exceeds £1.50 with a similar case for SD subscription being £0.75.
Finally - in addition to the above, it must also be noted that this company is a daughter company from which we lease all our content from our parent company. The costs of the leases are £1 (per month) for HD subscription and £0.75 (per month) for SD subscription. Our aim is not to exceed £80 of leasing cost.

 

[HallsofIvy]

The way you have set this up is very confusing! You write

HD stream = 4 = x

when, in fact, "4" is a coefficient of x, not a value of x. You ask

How do I find that the HD subscriptions is twice as profitable?

You don't! You are told that

SD single screen” subscriptions given that it is 2 times more profitable to sell SD single screen subscriptions than HD single screen ones

in the first sentence of the problem.

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And what the HD and SD customers existing customers have o do with the problem?

They must be included in the "hardware limitations".
You are told

a server can only stream 200 IO streams, where a HD stream consumes 4 IO streams and a SD stream only consumes 1 IO stream.

So, letting x be the number of new HD streams and y the number of new SD streams, 4(x+ 5)+ (y+ 10)= 4x+ y+ 30<= 200 or 4x+ y<= 170.

Finally - in addition to the above, it must also be noted that this company is a daughter company from which we lease all our content from our parent company. The costs of the leases are £1 (per month) for HD subscription and £0.75 (per month) for SD subscription. Our aim is not to exceed £80 of leasing cost.

So x+ 0.75y<= 80

You want to maximize 2x+ 2 subject to those constraints.

The part I can't make sense of is

In terms of bandwidth cost, we have a simple contract that provides the first £100 worth (per month) of bandwidth free, after which the cost for bandwidth significantly increases such that users do not exceed this free £100 limit. It is to be noted that on average the bandwidth consumption (per month) of a typical HD subscription never exceeds £1.50 with a similar case for SD subscription being £0.75.

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Is the

first £100 worth (per month) of bandwidth

per customer or total? I first read it as if it were per customer but if that is the case, the "

£1.50" and​

"£0.75" are so low compared to the "£100" that it is irrelevant. If it is total, then we have the additional constraint "0.75y+ 1.5x<= 100".​

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