Linear Programming

Dear Sir Moffat, Hope you are ok.
I love your lectures and believe they are very helpful. But today i was very confused when practicing past exam papers and here is the reason why…

Could you please help and explain why is that i can’t go this way like you explained in lectures.

0.5P+0.75S?12000
0.27P+0.27S?5400

then the first equation multiply by 0.54 in order to get both Ps equal to 0.27 and then substract and finally end up with P=8000

why is that the examiner calculates it this way S = 12,000
0·5P + 0·75S = 12,000

????

The question tells about the Higgins Co (HC).
I won’t be able to paste the whole question up here so i have paste the link leading down below.

http://upload.news.esnai.com/2013/0326/1364284369236.pdf – the link for the question#2

http://upload.news.esnai.com/2013/0326/1364282908799.pdf – the link for the answers

I hope and will look forward to get the assistance from you so i can understand this topic right and pass the exam.

Thanks in advance.