A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters.
2007-12-22 15:48:26 · 5 answers · asked by kingtekrin 2 in Science & Mathematics ➔ Mathematics
Howdy. :) Season's greetings and Happy New Year! :) I sure hope all is well. :) As for the question, I've done my best to explain the solution below:
Let X = Scarves
Let Y = Sweaters take 14 hours
Given:
It takes 02 hours to produce 1 scarf
It takes 14 hours to produce 1 sweater
We can calculate that:
It takes 04 hours to produce 02 scarves.
It takes 06 hours to produce 03 scarves.
It takes 10 hours to produce 05 scarves.
It takes 28 hours to produce 02 sweaters.
It takes 42 hours to produce 03 sweaters (which exceeds the number of available hours!).
It takes 56 hours to produce 04 sweaters (which also exceeds the number of available hours!).
and that:
05 scarves (X) + 0 sweaters (Y) <= 5 items
04 scarves (X) + 01 sweater (Y) <= 5 items
03 scarves (X) + 01 sweater (Y) <= 5 items
03 scarves (X) + 02 sweaters (Y) <= 5 items
02 scarves (X) + 02 sweaters (Y) < 5 items
01 scarf (X) + 02 sweaters (Y) < 5 items
01 scarf (X) + 01 sweater (Y) < 5 items
So, the possible inequalities that can satisfy this situation are:
5X + 0Y <= 5
4X + Y <= 5
3X + Y <= 5
3X + 2Y <= 5
2X + 2Y <= 5
X + 2Y < 5
X + Y < 5
Given the available time and item production limit, their greatest production output is confined to 5 scarves or 3 scarves and 2 sweaters at most!
I sure hope that helps. :) Good luck and take care. :)
Cheers! :)
Cogano
2007-12-22 17:01:58 · answer #1 · answered by Cogano 3 · 0⤊ 0⤋
2x + 14y = 40 (# of scarfs times 2 hours it takes to make them + # of sweaters and how long it takes to make them = 40 total hours)
x + y = 5 (scarfs + sweaters = 5 total items)
2007-12-22 23:56:24 · answer #2 · answered by An average girl <3 3 · 0⤊ 0⤋
2x + 14y ⤠40
x + y ⤠5
2007-12-23 00:10:15 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋
2x+14y=40
x+y=5
2007-12-22 23:52:43 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Check out this solution
http://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.92912.html%22
2007-12-22 23:53:30 · answer #5 · answered by Jim 5 · 0⤊ 0⤋