# ACCA F5 query

Registered Posts: 354
I'm currently working through linear programming problems and I'm confused about one particular aspect.

I have a constraint expressed as 2x < 3y and I'm not entirely sure what it actually means.

My study text says when x = 3 then 3y = 6 and hence y = 2.

What does that mean? Does it mean 3 units of product x is produced and so y must be twice as much to equal 6 untis? Where is y = 2 coming from?

I'm afraid to say the explanations in my BPP study text are simply below par.

Thanks for any help

Mark

• Registered Posts: 258 π π π
Without seeing the definitions in the original problem you can not tell what the practical solution is, y and x must be defined somewhere.

But what you have here a a straight forward piece of algerbra where y is a dependant (depending on the value of x) and x is a variable. The linear formula is expressed as a limiting formula rather than an equality, so whatever physical items x and y are, the formula tells us that

two lots of x are less than 3 lots of y,
so if x = 3

then

2 lots of 3 are less than 3 lots of y,

divide both sides by 3

(2 lots of 3)/3 is less than 3/3 lots of y; or
2 is less than y, or 2<y

by formula

2x<3y
if x=3
(2*3)<3y
2<y
• Registered Posts: 1,954
mark057 wrote: Β»
I have a constraint expressed as 2x < 3y and I'm not entirely sure what it actually means.

My study text says when x = 3 then 3y = 6 and hence y = 2.

x and y can represent anything.

3y = 6 so y must be equal to 2. ie 3 times 2 = 6.
• Registered Posts: 981
stevef wrote: Β»
Without seeing the definitions in the original problem you can not tell what the practical solution is, y and x must be defined somewhere.

But what you have here a a straight forward piece of algerbra where y is a dependant (depending on the value of x) and x is a variable. The linear formula is expressed as a limiting formula rather than an equality, so whatever physical items x and y are, the formula tells us that

two lots of x are less than 3 lots of y,
so if x = 3

then

2 lots of 3 are less than 3 lots of y,

divide both sides by 3

(2 lots of 3)/3 is less than 3/3 lots of y; or
2 is less than y, or 2<y

by formula

2x<3y
if x=3
(2*3)<3y
2<y

x=1 y >2/3
x=2 y>4/3
x=3 y> 6/3 = 2
x=4 y>8/3

erc so you can see kind of like a progression if you do x in the horitzonal axis and y in the vertical then you can plot the above inequality 2x<3y

Lets assume both x and y are positive x>0, y>0 then the above drawing in the XY axis will give you an area of points that are true , ie verify the 2x<3y

3y -2x>0

so for examlpe y= number of pillows and x number of carpets lets say 3 pounds per pillow and 2 pounds per carpet then the above gives you all the different pairs (x,y) how many carpets and pillows you can buy ...
• Registered Posts: 354
Just one other question from the book.

Question: Brunel manufactures plastic-covered steel fencing in two qualities, standard and heavy gauge. Both products pass through the same processes, involving steel-forming and plastic bonding.

Standard gauge fencing sells at \$18 a roll and heavy gauge fencing at \$24 per roll. Variable costs per roll are \$16 and \$21 respectively. There is an unlimited market for the standard gauge, but demand for the heavy gauge is 1300 rolls per year. Factory operations are limited to 2400 hours a year in each of the two production processes.

Gauge Steel-forming Plastic bonding
Standard 0.6 0.4
Heavy 0.8 1.2

I've managed to work out most of the answer but something in the solution is puzzling me. The solution states the obejective is to maximise 2S + 3H.

Why 2S + 3H. Why not just S + H? Is there some way of using the data above to determine 2S + 3H?

Any help would be greatly appreciated.
• Registered Posts: 1,954
Is that whole of the question?

Or I must be missing something..
• FMAAT, AAT Licensed Accountant Posts: 4,071 π π π
My useless contribution for the day:
I'm glad I'm not doing ACCA.

3y = 6 so y must be equal to 2. ie 3 times 2 = 6.
I get that.

How 2x < 3y when x=3 and y=2 I don't know. 6 = 6 in my book and I don't want any book that says otherwise!!

*runs away and hides*
• Registered Posts: 465
mark057 wrote: Β»
Just one other question from the book.
Why 2S + 3H. Why not just S + H? Is there some way of using the data above to determine 2S + 3H?

Any help would be greatly appreciated.

Mark, the idea of this topic is to determine the best mix of products to make. You want to make as much profit/contribution as possible with the resources you have available. In this question, the contribution of the standard roll is \$2 per unit (\$18-\$16) and the contribution of the heavy rolls is \$3 (\$24-\$21).

You are going to make S units of the standard and H units of the heavy - S and H being the amounts you are going to calculate - if it helps relabel them x and y if you are used to variables being x and y from maths. So the contribution you will make from the products you make will be the number of standard rolls times \$2 per unit - 2S - plus the number of heavy rolls times \$3 per unit - 3H. So 2S + 3H in total.
• Registered Posts: 354
Thank you all for your posts.

I'm using a BPP study text and i'm not very impressed with it at all.

It shows the workings but their is no underlying explanation for the calculations.

I skipped through my AAT management accountancy papers but this thing is seriously testing my patience.

I'm going to a BPP open day in Feb and will be pointing out the deficiencies of this text.

Mark
• Registered, Tutor Posts: 131 π π π
Mark,

I'm working through the same BPP F5 text and have looked again at the question you mentioned, getting worried I'd missed something! Decided that it looks worse than it is, once I realised contribution was the key word I could follow the text fine. Don't give up! I can only suggest what works for me, actually work through all the examples don't just read them, write out your own calculations and comments as you go through it.

Do you also have the practice and exam kit? I always find doing as many questions as possible helps because you get used to how they are worded and are able to pick out what is needed, can be very useful to try a question yorself then compare it to the given answer and work through this to ensure you understand it. Maybe try getting the Kaplan exam kit to for additional practice, that's what I did for F4 and it seemed to work for me.

I've found it a big step up from the AAT papers (especially as I did them 5 years ago!!)