**The problem is:**

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.

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.

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 existing customers have to do with the problem?

IO streams = 200

HD stream = 4 = x

SD stream = 1 = y

4x + 1y = 200

=y=200-4x

X intercepts (50,0) Y intercepts (0,200)

Bandwidth cost = 100

1.50 HD x 0.75 SD Y

1.5x + 0.75y = 100

y=2(3-x+200)/3 X intercepts (200/3) Y intercepts (0, 400/3)

Which I believe is related to the profitability X being twice as profitable than Y.

Lease cost =80

HD = 1 x

SD = 0.75y

1x + 0.75y = 80

y=4(-x+80)/3

X intercepts (80,0) Y intercepts (0,320/3)

Am I doing the correct calculations?

Many thanks in advance for any help.