Maximization

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Krenoshi

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A teenage club makes two types of gadgets. The manufacturing of each gadget requires two
operations: Assembly and Finishing. Gadget A requires 1 hour of Assembly and 2 hours of
Finishing. Gadget B requires 2 hours of Assembly and 1 hour of Finishing. The total work-hours
available per week in the Assembly is at most 10, and in the Finishing, at most 8. If a profit of
$25 is realized for every A gadget, and $30 for every B gadget,
a. how many of each should be manufactured to maximize profit, and
b. what is the maximum profit?
______________________________________________________________________________________
All the problems I have had like this has had assembly and finishing the same. i.e. 60 hours of assembly and 60 hours of finish. This one is different. so x+2y<=60 & 2x+y<=60
So I am not sure what the constraints are.
Is it:
x+2y<=10
2x+y<=10
Where does the at most 8 hours of finishes come in?
 
Krenoshi said:
A teenage club makes two types of gadgets. The manufacturing of each gadget requires two
operations: Assembly and Finishing. Gadget A requires 1 hour of Assembly and 2 hours of
Finishing. Gadget B requires 2 hours of Assembly and 1 hour of Finishing. The total work-hours
available per week in the Assembly is at most 10, and in the Finishing, at most 8. If a profit of
$25 is realized for every A gadget, and $30 for every B gadget,
a. how many of each should be manufactured to maximize profit, and
b. what is the maximum profit?
______________________________________________________________________________________
All the problems I have had like this has had assembly and finishing the same. i.e. 60 hours of assembly and 60 hours of finish. This one is different. so x+2y<=60 & 2x+y<=60
So I am not sure what the constraints are.
Is it:
x+2y<=10
2x+y<=10
Where does the at most 8 hours of finishes come in?
Click to expand...

Define your variables. What is x? What is y?

How did you get 2x + y ≤ 10?
 
Subhotosh Khan said:
Define your variables. What is x? What is y?

How did you get 2x + y ≤ 10?
Click to expand...

Gadget A = x
Gadget B = y

I don't know where to begin on this one. To many variables for me.. assembly, finish, 10 hours max assembly and 8 hours max finish :confused::confused::confused:
 
Krenoshi said:
Gadget A = x
Gadget B = y

I don't know where to begin on this one. To many variables for me.. assembly, finish, 10 hours max assembly and 8 hours max finish :confused::confused::confused:
Click to expand...

You say:

Gadget A = x
Gadget B = y

What of gadget A is equal to x? Color? Height? Weight?

What of gadget B is equal to y? Color? Height? Weight?
 
Subhotosh Khan said:
You say:

Gadget A = x
Gadget B = y

What of gadget A is equal to x? Color? Height? Weight?

What of gadget B is equal to y? Color? Height? Weight?
Click to expand...

Nevermind. I am already confused with this problem as it is. Thanks for replying though.
 
Krenoshi said:
Nevermind. I am already confused with this problem as it is. Thanks for replying though.
Click to expand...
You just need to define your variables clearly so that we know what they are representing.
Here, it seems you are defining them this way:
x = the number of Gadget A produced
y = the number of Gadget B produced

Your first constraint is correct. Your second constrain should have an 8 where you have 10.
 
Harry_the_cat said:
You just need to define your variables clearly so that we know what they are representing.
Here, it seems you are defining them this way:
x = the number of Gadget A produced
y = the number of Gadget B produced

Your first constraint is correct. Your second constrain should have an 8 where you have 10.
Click to expand...

So it would be?

x+2y<=10
2x+y<=8

Both gadgets have assembly time and finish time. Why does one have an 8 and not the other?
 
Krenoshi said:
Nevermind. I am already confused with this problem as it is. Thanks for replying though.
Click to expand...
Excuse me but Subhotosh's question to you was right on target. If you do not know what YOUR variables represent you can't do the problems. You were able to set up your other problems because you just blindly followed a pattern that was working but did not understand what you were doing. Subhotosh was trying to get you to understand how to do these problems. However you just want the answer without any understanding. This is not what this forum is about. The helpers on this forum want you to understand what is going on so if a number like 10 becomes an 8 it will not confuse you. I think that you owe Subhotosh an apology and also need to rethink how you learn math.
 
Harry_the_cat said:
You just need to define your variables clearly so that YOU know what they are representing.
Here, it seems you are defining them this way:
x = the number of Gadget A produced
y = the number of Gadget B produced

Your first constraint is correct. Your second constrain should have an 8 where you have 10.
Click to expand...
See in red. Your response was nice, I just made it nicer for the OP. Peace!
 
Krenoshi said:
So it would be?

x+2y<=10
2x+y<=8

Both gadgets have assembly time and finish time. Why does one have an 8 and not the other?
Click to expand...

READ the question.

"The total work-hours available per week in the Assembly is at most 10, and in the Finishing, at most 8."

x+2y represents the work-hours for Assembly (very important that you understand this)

and

2x+y represents the work-hours for Finishing (ditto)
 
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