SOLUTION: A small clothing company makes two types of jeans - straight cut and flare cut. Straight-cut jeans require 10 min of cutting time and 15 min of sewing time. Flare cut jeans re

Algebra ->  Inequalities -> SOLUTION: A small clothing company makes two types of jeans - straight cut and flare cut. Straight-cut jeans require 10 min of cutting time and 15 min of sewing time. Flare cut jeans re      Log On


   

Question 1193040: A small clothing company makes two types of jeans - straight cut and flare cut. Straight-cut jeans require 10 min of cutting time and 15 min of sewing time. Flare cut jeans require 20 min of cutting time and 10 min of sewing time. The company has a maximum of eight hours of cutting time and 10 hours of sewing time available each day.
Let x represent the number of straight cut jeans made in a day.
Let y represent the number of flare cut jeans made in a day.
Determine a system of Linear Inequalities that model this situation.

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
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A small clothing company makes two types of jeans - straight cut and flare cut.
Straight-cut jeans require 10 min of cutting time and 15 min of sewing time.
Flare cut jeans require 20 min of cutting time and 10 min of sewing time.
The company has a maximum of eight hours of cutting time and 10 hours of sewing time available each day.
Let x represent the number of straight cut jeans made in a day.
Let y represent the number of flare cut jeans made in a day.
Determine a system of Linear Inequalities that model this situation.
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In this problem, you have TWO restrictions.

One restriction is for cutting time; other restriction is for sewing time.



For x straight cut jeans and y flare cut jeans, the cutting time is 10x + 20y minutes.

So, your first inequality is

    10x + 20y <= 480 minutes  (1)   (480 minutes is 8 hours = 8*60 minutes = 480 minutes).



For x straight cut jeans and y flare cut jeans, the sewing time is 15x + 10y minutes.

So, your second inequality is

    15x + 10y <= 600 minutes  (2)   (600 minutes is 10 hours = 10*60 minutes = 600 minutes).



Thus two restrictions are 

    10x + 20y <= 480 minutes  (1)    (cutting time)

    15x + 10y <= 600 minutes  (2)    (sewing time).



The rest restrictions are standard inequalities of non-negativity

    x >= 0,  y >= 0.



At this point, the setup is complete and the problem posed in the post is solved.


The standard mantra when making setup is to say  " write inequalities as you read the problem ".

By pronouncing this mantra and doing accordingly,  you always will be on the way to success.


                This mantra is your  ENGINE.

        This solution in your head is your  TEMPLATE.