Linear Programming and Systems! HELP!

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needmathhelpp

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Oct 11, 2012
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This problem is so hard. I can't figure it out! I've been on it for almost an hour and I'm in desperate need of help ):
.

ResourcesPlant 1 (Hours per system)Plant 2 (hours per system)
Motherboard Production91
Technical Labor93
General manufacturing48




 
Last edited:
needmathhelpp said:
This problem is so hard. I can't figure it out! I've been on it for almost an hour and I'm in desperate need of help ):
"A gaming manufacturing company has developed a new gaming system. To produce the new system, they plan on using resources in two manufacturing plants. The table gives the hours needed for three tasks. For both plants combined, the company has allocated the following resources on a weekly basis: 1700 h of motherboard production, 1800h of technical labor, and 2400 h of general manufacturing. The first plant earns a profit of $90 per gaming system and the second plant earns $70 per system.

ResourcesPlant 1 (Hours per system)Plant 2 (hours per system)
Motherboard Production91
Technical Labor93
General manufacturing48

Use the information above to determine how many gaming systems the company should make in each plant to maximize profit.
1. Create an objective function for the profit P that the company can earn. Let x represent the number of gaming systems that will be made in Plant 1, and let y represent the number of gaming systems that will be made in plant 2.
(My answer - P(x,y)=90x +70y

2. Write a constraint function for each of the resources and for any contextual contraints that you identify. (Hint. THere are 5 of these, 2 are common sense)
(What I have x_>0 & y_>0) I NEED HELP WITH THIS!

3. Graph the constraint functions. Then use systems of equations to find the vertex points of the feasibility region
4. Which vertex point maximizes profit with the given constraints?
5. What is the max profit that the company can make with the given constraints? How many gaming systems should each plant make to maximize profit?
I know how to do all of this, but I Just can't figure out what the constraint function would be!
Click to expand...

Constraints: 1700 h of motherboard production, 1800h of technical labor, and 2400 h of general manufacturing. So, 1700, 1800 and 2400 go in the far right column of your table. Next write one constraint equation (inequality) for each row. The first one would be 9x + y is less than or equal to 1700. Make sense?

Next, graph these and test the vertices/intersection points in your Profit equation.
 
needmathhelpp said:
This problem is so hard. I can't figure it out! I've been on it for almost an hour and I'm in desperate need of help ):
"A gaming manufacturing company has developed a new gaming system. To produce the new system, they plan on using resources in two manufacturing plants. The table gives the hours needed for three tasks. For both plants combined, the company has allocated the following resources on a weekly basis: 1700 h of motherboard production, 1800h of technical labor, and 2400 h of general manufacturing. The first plant earns a profit of $90 per gaming system and the second plant earns $70 per system.

Resources
Plant 1 (Hours per system)
Plant 2 (hours per system)
Motherboard Production
9
1
Technical Labor
9
3
General manufacturing
4
8

Use the information above to determine how many gaming systems the company should make in each plant to maximize profit.
1. Create an objective function for the profit P that the company can earn. Let x represent the number of gaming systems that will be made in Plant 1, and let y represent the number of gaming systems that will be made in plant 2.
(My answer - P(x,y)=90x +70y Correct

2. Write a constraint function for each of the resources and for any contextual contraints that you identify. (Hint. THere are 5 of these, 2 are common sense)
(What I have x_>0 & y_>0) These are correct: they are the "common sense" constraints. You can't produce a negative number of gaming systems.

I NEED HELP WITH THIS!

3. Graph the constraint functions. Then use systems of equations to find the vertex points of the feasibility region
4. Which vertex point maximizes profit with the given constraints?
5. What is the max profit that the company can make with the given constraints? How many gaming systems should each plant make to maximize profit?
I know how to do all of this, but I Just can't figure out what the constraint function would be!
Click to expand...
What is the maximum number of hours available for production of motherboards required by the gaming systems? Hint: the problem tells you. You just have to read.

What function using x and y will tell you how many hours are actually used in the production of motherboards? This takes just a bit of creativity.

Can you put those two pieces of information into a relationship? What is that relationship?
 
Show us your three equations solved for y.

Tell us what calculator you're using.

Tell us the window settings on your graph.
 
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needmathhelpp said:
I did this before I posted on here, but when I solved for y and put it in my graphing calculator it was a big mess! ):
9x +1y <_ 1700 This is correct
9x+3y<_ 1800 As is this
4x +8y <_ 2400 And this
Click to expand...

needmathhelpp said:
feasible region was a quadrilateral, in quadrant 1, and one of it's side is on the y axis!
Click to expand...
So you should have FIVE lines representing constraints. One of those lines is the y-axis because x must be non-negative, and one should be the x-axis because y must be non-negative. So you definitely SHOULD be in quadrant 1.
 
You like charades? :cool:

I did get the one answer to my three questions, but I'd like to know what are the expressions that you entered for Y1=, Y2=, Y3=?

If you also tell me your window settings (no scales), that may save us from each typing an extra post. Cheers
 
vBulletin Hint: If you would like to delete a post, you may go to the post's edit page and find the delete option near the top of the page. :cool:
 
needmathhelpp said:
I'll pm you it
Click to expand...

Ahhh, you're shy. :)

Really, there's no need for that. (Are we being watched?)

I cannot speak for other volunteers, but tutoring by private message is one of my lowest priorities. That would be too much like a delayed chat-room atmosphere for me; these boards are not a chat room.

People post questions or work, and we provide appropriate feedback.
 
I'm multi-tasking ... why are you graphing all the way out to x = 2000? Why are you looking at 200 x units in Quadrant II ? (that's negative territory: x>=0)

If you were to increase the scales from 5, you'd be able to see tick marks on the scales -- which would allow you to guesstimate a new set of windows settings to use.

Looks to me like you should try some settings like these:

xMin 0

xMax 225

xScale 25

yMin 0

yMax 325

yScale 25


The TI-84 will only display decimal numbers, unless there's a built-in conversion function to a Rational number. I'd have to look that up. Do you have a user's manual?
 
By the way, your instructions (thanks to Bill) require that you find the vertex coordinates by solving systems of equations, versus asking TI-84.

You've done that already?
 
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