Word Problem, maximise profits, solve using Linear Programming?

[glaceau]

a small business makes laptops and notepads. In any given month labour costs must not exceed £1350 and material costs must be a maximum of £1150.

Relevant information:
Laptops cost £50 in materials to make and labour costs £50, they make £110 profit on each laptop.
notepads cost £25 in materials to make and labour costs £40, they make £70 profit on each notepad.

QUESTION: HOW MANY OF EACH TYPES OF COMPUTER SHOULD THE COMPANY AIM TO SELL EACH MONTH IN ORDER TO MAKE THE MAXIMUM PROFIT?

Thanks if anybody can answer this question! :shock:

 

[Deleted member 4993]

a small business makes laptops and notepads. In any given month labour costs must not exceed £1350 and material costs must be a maximum of £1150.

Relevant information:
Laptops cost £50 in materials to make and labour costs £50, they make £110 profit on each laptop.
notepads cost £25 in materials to make and labour costs £40, they make £70 profit on each notepad.

QUESTION: HOW MANY OF EACH TYPES OF COMPUTER SHOULD THE COMPANY AIM TO SELL EACH MONTH IN ORDER TO MAKE THE MAXIMUM PROFIT?

Thanks if anybody can answer this question! :shock:

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting!!

 

[glaceau]

Thank you. I know that Objective function is to work out how many of each computer to sell.

Constraints are Labour must be less or equal to 1350 and materials must be less or equal to 1150

after that I don't know what to do :neutral:

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting!!

 

[Deleted member 4993]

a small business makes laptops and notepads. In any given month labour costs must not exceed £1350 and material costs must be a maximum of £1150.

Relevant information:
Laptops cost £50 in materials to make and labour costs £50, they make £110 profit on each laptop.
notepads cost £25 in materials to make and labour costs £40, they make £70 profit on each notepad.

QUESTION: HOW MANY OF EACH TYPES OF COMPUTER SHOULD THE COMPANY AIM TO SELL EACH MONTH IN ORDER TO MAKE THE MAXIMUM PROFIT?

Thanks if anybody can answer this question! :shock:

Assume:

The # of Laptops made = L

The # of Notepads made = N

P(rofit) = L*110 + N*70 ← This is the function you need to maximize.

Now write the constraints as mathematical functions - in terms of L & N.

Continue...

 

[glaceau]

Assume:

The # of Laptops made = L

The # of Notepads made = N

P(rofit) = L*110 + N*70 ← This is the function you need to maximize.

Now write the constraints as mathematical functions - in terms of L & N.

Continue...

Labour costs 50X + 40Y will be equal to or less than 1350
Material costs 50X + 25Y will be equal to or less than 1150

5X + 4Y = 135


and


2X + 1Y = 46


I feel lost really?

 

[glaceau]

Start by "seeing" what happens if maximum material and labor are used:
50L + 25N = 1150
50L + 40N = 1350

Solve for L and N.
Carry on from that...

I've sort of worked out that producing 15 L and 15 N would result in labour costs of 1350 and material costs of 1125.

Giving a profit of £2700.

I see to be within the constraints (Exactly for labour and just 25 less than the materials maximum spend), I've sort of worked it out in my head though, I ideally want to be able to do it on a graph and know what I'm doing!

How does my answer sound?

 

[glaceau]

Thank you.

By a process of trial and error I'm fairly confident that profits can be maximised by producing

17L and 12N and this level of production falls within the constraints ?

However, I'm really, really lost in how I show this in a graph and also what I "plug in"

These are some of the "plot lines" I gained in class................But it's nonsensical to me!

What you think?

5X + 4Y = 135

X = 19 Y = 10
X = 23 Y = 5
X = 11 Y = 2-

2X + 1Y = 46

X = 23 Y = 0
X = 0 Y = 46
X =15 Y = 16

I'VE GOT SOMETHING DONE I GUESS! Does a max profit of 2710 sound correct? Based on 17L & 12N sold, Labour = 1330 & materials = 1150

Thanks

 

[glaceau]

Thanks