1. ## inequalities linear programming

Hello eveyone!

two machines:
type A costs £50 per day and needs one person to operate it,
type B costs £20 per day and needs 4 people to operate it

let x be the number of type A
let y be the number of type B

1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
2. a contractor can spend up to £1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

thanks!

2. I had a go, and obviously, x+4y has to be equal to or less that 64 because that is teh workforce.

64 has factors, 2, 4,8,16,32. so if x=2, 4y must be 62, but we can't get 62 so x can never be 2. is x=4, 4y must be 60 so y =15

-am i on the right lines? I can't see how I would manipulate the algebra to answer this one.

3. Originally Posted by Sweeties
I had a go, and obviously, x+4y has to be equal to or less that 64 because that is teh workforce.
Yes, and that is all that is needed to answer 1. What follows is waffle.

64 has factors, 2, 4,8,16,32. so if x=2, 4y must be 62, but we can't get 62 so x can never be 2. is x=4, 4y must be 60 so y =15

That those are the factors of 64 has nothing to do with what you then write.

If x=2 then y=15 satisfies the constaint, so x can be 2 (at least as far as the workforce constraint is concerned.

Now what are you trying to do? This is not answering either of the questions asked.

RonL

4. Originally Posted by CaptainBlack
Yes, and that is all that is needed to answer 1. What follows is waffle.

That those are the factors of 64 has nothing to do with what you then write.

If x=2 then y=15 satisfies the constaint, so x can be 2 (at least as far as the workforce constraint is concerned.

Now what are you trying to do? This is not answering either of the questions asked.
.

RonL
OK, I haven't a clue how to answer this question. The waffle was me having a go at it.

Here's me having aother go:

x+4y < 64 (take < to mean less than or equal to plz)

4y < 64-x

y= (64-x)/4

y= 16 -x/4

substitute into original equaion:

x+ 4(16-x/4) <64

x+ 64 -x <64

64 < 64

I get 64 is less than or equal to 64. Stumped.

5. Originally Posted by Sweeties
Hello eveyone!

two machines:
type A costs £50 per day and needs one person to operate it,
type B costs £20 per day and needs 4 people to operate it

let x be the number of type A
let y be the number of type B

1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
2. a contractor can spend up to £1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

thanks!
The bold bit are the two questions.

6. Originally Posted by Sweeties
Hello eveyone!

two machines:
type A costs £50 per day and needs one person to operate it,
type B costs £20 per day and needs 4 people to operate it

let x be the number of type A
let y be the number of type B

1. a contracter has a labour force of 64 people, explain why x+4y is less than or equal to 64
2. a contractor can spend up to £1040 per day on hiring machines, explain why 5x+2y is less than or equal to 104

thanks!
$x+4y\leq64$ because you only have 64 possible workers, as you mentioned. If $x+4y>64$, then you won't have enough workers to operate all of the machines.

Similarly for the second question, you have $5x+2y\leq104$. You get this because $50x+20y\leq1040$, where the left side is the amount of money needed to operate the machine, and the right side is your budget. Since you cannot exceed \$1040, you know the inequality to be true, and you can easily see that $50x+20y\leq1040\implies\frac{50}{10}x+\frac{20}{10 }y\leq\frac{1040}{10}\implies5x+2y\leq104$.