SOLUTION: please put this problem in a system of inequalities and draw a graph AM radios takes 15 hrs. to produce AM/FM takes 20 hrs to produce the production hrs are limited to 300 hrs per

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: please put this problem in a system of inequalities and draw a graph AM radios takes 15 hrs. to produce AM/FM takes 20 hrs to produce the production hrs are limited to 300 hrs per      Log On


   

Question 60305: please put this problem in a system of inequalities and draw a graph
AM radios takes 15 hrs. to produce AM/FM takes 20 hrs to produce the production hrs are limited to 300 hrs per week the plant's capacity is limited to a total of 18 radios per week and existing orders requires that a least 4 Am radios and 3AM/FM radios be produced per week. x is the number of AM radios and y is the number of AM/FM radios. I would really appreciate help because I do not know where to start. Thank you for your help!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
please put this problem in a system of inequalities and draw a graph
AM radios takes 15 hrs. to produce AM/FM takes 20 hrs to produce the production hrs are limited to 300 hrs per week the plant's capacity is limited to a total of 18 radios per week and existing orders requires that a least 4 Am radios and 3AM/FM radios be produced per week. x is the number of AM radios and y is the number of AM/FM radios
:
Let x = no. of AM radios; Let y = no.of AM/FM radios
:
"The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week."
The hour equation:
15x + 20y =< 300
Arrange it "y=" in order graph it
20y =< 300 - 15x
y =< 300/20 - (15/20)x
y =< 15 - .75x; plotted as the red line
:
"The plant’s capacity is limited to a total of 18 radios"
The quantity equation:
x + y <= 18
y <= 18 - x; plotted as the green line
:
"At least 4 AM Radios"
x => 4
This will be vertical line parallel to y axis, passing thru x =>4. You will have
to draw this in yourself
:
"At least 3 AM/FM Radios"
y => 3, plotted as the black line
:
The graph:
+graph%28+300%2C+200%2C+-4%2C+20%2C+-4%2C+20%2C+15+-.75x%2C+18-x%2C+3+%29+

:
Note that the feasibility region would be bounded by:
1. area equal or above the horizontal line going thru y = 3,
2. the vertical line that you will draw going thru x = 4, or to the right,
3. Equal or below the red and the green lines whichever is lowest.
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