Math Is Fun Forum

ndescandon

Member

Registered: 2007-07-05

Posts: 1

Draw the appropriate graphs in each of the following.

Draw the appropriate graphs in each of the following. ok I have been trying to draww a graph but I can't seem to it right and can someone see if my answer is right   

20. A small firm produces both AM and AM/FM car 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 plant’s capacity is limited to a total of 18 radios per
week, and existing orders require that at least 4 AM radios and at least 3 AM/FM
radios be produced per week. Write a system of inequalities representing this situation.
Then, draw a graph of the feasible region given these conditions, in which x
is the number of AM radios and y the number of AM/FM radios.

In a system, x & y have to represent the same thing in all equations/inequalities. As you have it, in the first inequality X & Y are hours, and in the second it's radios.

X= number of AM radios
Y= number of AM/FM radios

15x+20y <= 300
x => 4
y => 3
x+y <=18

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Draw the appropriate graphs in each of the following.

Ah, good old Decision Maths. Easily my favourite of all the A-level mathses.
Anyway, it looks like you've got all your inequalities right (although I'm confused about how you can have a 300-hour week), so your graph should look something like this.
Hopefully you'll be able to see which line is which. I also put a grid in the feasible region, because you can only have integer amounts of radios. Amazing what you can do in Paint.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Draw the appropriate graphs in each of the following.

I'm confused about how you can have a 300-hour week

Why? Two radios can have a maximum production rate of 336 hours a week.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Draw the appropriate graphs in each of the following.

Well, I suppose. But it would be more logical to just put the amount of time that all radios can have, rather than adding the hours up for each one.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Draw the appropriate graphs in each of the following.

But how is the problem going to be solved if you don’t know how many hours have been worked for each product?

HallsofIvy

Guest

Re: Draw the appropriate graphs in each of the following.

Well, I suppose. But it would be more logical to just put the amount of time that all radios can have, rather than adding the hours up for each one.

If x+ y= 300 what are x and y?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Draw the appropriate graphs in each of the following.

Ah, now I get it. In that case, the way it's being done makes perfect sense.

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Why did the vector cross the road?
It wanted to be normal.