Algebra 2 linear programming word problem help asap!?

[roxursox]

The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at most 10 units of paper a day. At least 1 unit of newspaper is required daily by regular customers. The mill can run 24 hours a day. Producing a unit of notebook paper takes 1 hour, producing a unit of newspaper takes 4 hours. If the profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350, how many units of paper should the manager have the mill produce each day to maximize profits?

you must
1. define variables
2. determine a system of inequalities/constraints
3. graph a "feasible region"
4. find the coordinates of the vertices of the feasible region
5. determine the objective function
6. find which one of the vertices of the region will maximize or minimize your objective

i really need help! i was out of school for a week and i missed all of this in class and i'm so confused if anyone could help me by guiding me through the steps that would be amazing and i would love you forever! thank you!

 

[galactus]

Are you familiar with Excel Solver?. It is great for solving linear programming problems.


Anyway, use the given info to construct a system of inequalities.

Let x=number of units of notebook and let y=number of units of newsprint.


At most 10 units, altogether: $\displaystyle x+y\leq 10$

At least one unit of newsprint: $\displaystyle y\geq 1$

a negative number of notebooks can not be produced: $\displaystyle x\geq 0$

The number of units produced in a 24 hour period: $\displaystyle x+4y\leq 24$

The profit is what is to be maximized. this is the objective function: $\displaystyle P=500x+350y$


Without Excel, you can solve the equations for y and graph them.

Note their intersections. The vertices of this region will be your 'feasible region'.

You can find the coordinates of the vertices by setting the line equations equal to one another and solving for x and y.

Note the coordinates of these vertices. Plug them into the objective function for profit to see which gives the greatest value.

It would be a huge help to graph. Let me know what you arrive at.

 

[roxursox]

Thank you so much. However, I am not sure if my graph is correct. I got the corners (10,1), (25,0), (24,1), and (11,0). Is that correct?
How do you find the coordinates of the vertices of the feasible region algebraically?
Also, I'm not sure how to find which one of the vertices of the region will maximize the objective.

P.S. you are a fantastic help!