Question

- Setup linear equations from word problem.

Answer 1

A paint manufacturer produces 2 paints of different colour – red and blue. It takes 1 hour to mix a vat of paint regardless of colour. There are however only 40 hours available per week for mixing. The cost of producing a vat of red paint is €200 whilst the cost of producing a vat of blue paint is €100. Production costs are limited to €6000. The profit (which the manufacturer wishes to maximise) made on each vat of red paint sold is €50 and on each vat of blue paint sold it is €40.

Answer 2

I see the maximisation function is 50x + 40y.

But the constraints?

200x + ? = 6000?
100x + ? = 6000?

Answer 3

@agent0smith

Literally my last Q to ask on here!

Answer 4

Thought about

200 R + 100 B <=6000 production cost?

R + B <= 40 production time?

Answer 5

x+y <= 40?

Answer 6

i'm using descriptive variable names


R for no of red tins he makes in week
B for Blue

Answer 7

Thats not correct unfortunately, used Wolfram to check.

Answer 8

What do you mean you used WA to check that it's not correct?

Answer 9

http://www.wolframalpha.com/input/?i=200+R+%2B+100+B+%3C%3D6000,+R+%2B+B+%3C%3D+40,+R+%3E%3D+0,+B+%3E%3D+0

(20, 20) gives a max value for 50R + 40B of 1800.

Answer 10

i drew it, because MW hates me, and I got the same. must be wrong.

Answer 11

The one he posted yesterday had a different answer, too. I'm not seeing how, unless the book's answers are unreliable.

Answer 12

Agent you here man? :)

Answer 13

Yes

Answer 14

The solution offered in my book says:

Ans: z = 18003; Red = 20, Blue = 20

You think that 3 is a typo?

Answer 15

LOL how would a 3 even get in there when the profit function is 50x + 40y

Answer 16

So would the constraints be:

200x + 100y <=6000 production cost?

x + y <= 40 production time?

Answer 17

Don't forget

x >= 0
y >= 0

Answer 18

Yeah, that's the correct solution then.

Answer 19

Constraints*

Answer 20

Yeah, your book seems like it probably had some poor editing.

Answer 21

Sucks because that can really set you off!

Answer 22

Oh yeah, it's frustrating.