Thread: Linear Programming and Systems! HELP!

1. Linear Programming and Systems! HELP!

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.

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!

2. Re: Linear Programming and Systems! HELP!

I think your problem statement is a little vague. "Let x be the number of gaming systems that will be made in plant 1"-- in what time period? A day? A week? A year? Based on other information, I think we are supposed to assume the time period is a week. Then the parts of the problem begin to fit together. With this assumption, the number of hours for motherboard production per week is

$\displaystyle 9x + 1y$

so we must have

$\displaystyle 9x + 1y \le 1700$

The other constraints are similar.

3. Re: Linear Programming and Systems! HELP!

Well, I think it's the hours like 1700,1800, and 2400

4. Re: Linear Programming and Systems! HELP!

And the constant u listed is the one I had assumed before asking this.
I have 9x +1y <_ 1700
9x+3y<_ 1800
4x +8y <_ 2400
But when I solved for y and put in my graphing calculator it was a big mess

5. Re: Linear Programming and Systems! HELP!

Don't try to "solve for y" in problems like this. Did the problem statement ask for you to find the optimal solution? If not, you have met the requirements of the exercise.

There is an algorithm for finding the optimal solution in this type of problem, but the impression I get from reading your post is that you haven't studied it yet.

6. Re: Linear Programming and Systems! HELP!

Yeah, this is alg 2 hons. But that's not the whole problem.

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!

7. Re: Linear Programming and Systems! HELP!

Originally Posted by helpmemathhh
Yeah, this is alg 2 hons. But that's not the whole problem.

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!
It's constraint functions (plural), not constraint function (singular). The constraint functions are

$\displaystyle 9x + 1 y = 1700$

etc. Just change all the inequalities you listed into equalities.

8. nvm I figured out how to do it