# Help: figure out fourth constraint

#### grantit

##### New member
I am having a difficult time finding out how to find a set of constraints?

The word problem is as follow: The Bookholder Company manufacturers two types of bookcases out of oak and walnut. Model 01 reuires 5 board feet of oak and 2 board feet of walnut. Model 02 requires 4 board feet of oak and 3 board feet of walnut. A profit of $75 is made on Model 01 bookcase and a profit of$125 is made of Model 02 bookcase. The company has a supply of 1000 board feet of oak and 600 board ft. of walnut. The company has orders for 40 Model 01 bookcases and 50 Model 02 bookcases. These orders indicate the min. number the company must manufacture of each model.

Write the set of constraints
Write the objective function
Graph the set of constraints
Determine the number of bookcases of each type the company should manufacture in order to maximize the profits.
Determine the max. profit

#### Subhotosh Khan

##### Super Moderator
Staff member
Start with finding "what are the required variables (dependant) to be calculated"?

Those are the

# of Model1 book cases to be made = N

# of Model2 book cases to be made = M

Then

The variable that you need to maximize is ...???.

Now look at the available material

Model 01 reuires 5 board feet of oak & Model 02 requires 4 board feet of oak & The company has a supply of 1000 board feet of oak

So the first constraint equation

5*N + 4*M ≤ 1000......................................................(1)

What's next?

#### grantit

##### New member
2x + 3y < 600[/url]

#### grantit

##### New member
Subhotosh Khan said:
Start with finding "what are the required variables (dependant) to be calculated"?

Those are the

# of Model1 book cases to be made = N

# of Model2 book cases to be made = M

Then

The variable that you need to maximize is ...???.

Now look at the available material

Model 01 reuires 5 board feet of oak & Model 02 requires 4 board feet of oak & The company has a supply of 1000 board feet of oak

So the first constraint equation

5*N + 4*M ≤ 1000......................................................(1)

What's next?
2x + 3y < 600

#### Subhotosh Khan

##### Super Moderator
Staff member
Did you get all the constaints and the objective function?

#### grantit

##### New member
Subhotosh Khan said:
Did you get all the constaints and the objective function?
x>0; y>0

Objective function is P=Ax + By

I'm having problems finding the coordinates.

#### Subhotosh Khan

##### Super Moderator
Staff member
grantit said:
Subhotosh Khan said:
Did you get all the constaints and the objective function?
x>0; y>0...Incorrect

x ≥ 40

y ≥ 50

Objective function is P=Ax + By...P = 75*x + 125*y

I'm having problems finding the coordinates.

#### grantit

##### New member
Here goes: 5x + 4y = 1000
2x + 3y = 600
x=40
y=50

Substitue value of x and y into problem to get coordinates.

40,200
40,0
0,50
40.5, 173.3

Multiply coordinates into objective function.

Max. number brings most profit.

What do you think? :lol:

Subhotosh Khan said:
grantit said:
[quote="Subhotosh Khan":361h93m0]Did you get all the constaints and the objective function?
x>0; y>0...Incorrect

x ≥ 40

y ≥ 50

Objective function is P=Ax + By...P = 75*x + 125*y

I'm having problems finding the coordinates.
[/quote:361h93m0]

#### Subhotosh Khan

##### Super Moderator
Staff member
Don't think so...

I get the point of intersection to be (85.71, 142.9)

P =75*85.71 + 125*142.9 = 24285.71 at intersection.

Check P at other vertices and confirm maximum point.

Since these are not integer # - you need to check for integer numbers that are within the region.