Maximizing PC Set Options: Venn Diagram Equation in a Computer Shop

[fiksx]

Homework Statement

In a computer shop, there are $33$ PC set that are sold:


1. with 18 sets of PC have crystal screen PC included,

2. with 12 sets of PC have printer included,

3. with 6 sets of PC have scanner system included,

4. with 3 sets of PC that include all(printer, scanner system,

crystal screen pc)

Relevant Equations

x=33-(18-(a+b+3)+12-(a+c+3)+6-(b+c+3) + ( a+b+c +3 ) )

In a computer shop, there are $$33$$ PC set that are sold:

1. with 18 sets of PC have crystal screen PC included,
2. with 12 sets of PC have printer included,
3. with 6 sets of PC have scanner system included,
4. with 3 sets of PC that include all(printer, scanner system,
crystal screen pc)

We want to find $$x$$ which is $$33-|S_1 \cup S_2 \cup S_3|=x$$ and get $$x$$ that is max

From the graph :
It means that inside $$18$$ crystal screen PC, there is a set that also includes a scanner or printer and, there is a set that contains only crystal screen.

1. $S_1\implies 18=a+b+3+$ crystal screen only
2. $S_2\implies 12 = a+c+3+$ printer only
3. $S_3\implies 6=b+c +3+$ scanner only

$$x=33-(18-(a+b+3)+12-(a+c+3)+6-(b+c+3) + ( a+b+c +3 ) )=x\\
33-(27-a-b-a-c-b-c + (a+b+c+3))=\\
33-(30 -a-b-c)=\\
3+a+b+c =x\\
a+b+c=x-3$$

More conclusions:

- $$a+c \le 9$$
- $$b+c \le 3$$
- $$a+b \le 15$$

What is the relation with $$x$$ and how do I get the actual result?

 

[Mark44]

Homework Statement:: In a computer shop, there are $33$ PC set that are sold:1. with 18 sets of PC have crystal screen PC included,

2. with 12 sets of PC have printer included,

3. with 6 sets of PC have scanner system included,

4. with 3 sets of PC that include all(printer, scanner system,

crystal screen pc)
Homework Equations:: x=33-(18-(a+b+3)+12-(a+c+3)+6-(b+c+3) + ( a+b+c +3 ) )

In a computer shop, there are $$33$$ PC set that are sold:

1. with 18 sets of PC have crystal screen PC included,
2. with 12 sets of PC have printer included,
3. with 6 sets of PC have scanner system included,
4. with 3 sets of PC that include all(printer, scanner system,
crystal screen pc)
View attachment 255373We want to find $$x$$ which is $$33-|S_1 \cup S_2 \cup S_3|=x$$ and get $$x$$ that is max

From the graph :
It means that inside $$18$$ crystal screen PC, there is a set that also includes a scanner or printer and, there is a set that contains only crystal screen.

1. $$S_1\implies 18=a+b+3+$$$$crystal screen only$$
2. $$S_2\implies 12 = a+c+3+$$ $$printer only$$
3. $$S_3\implies 6=b+c +3+$$ $$scanner only$$

$$x=33-(18-(a+b+3)+12-(a+c+3)+6-(b+c+3) + ( a+b+c +3 ) )=x\\
33-(27-a-b-a-c-b-c + (a+b+c+3))=\\
33-(30 -a-b-c)=\\
3+a+b+c =x\\
a+b+c=x-3$$

More conclusions:

- $$a+c \le 9$$
- $$b+c \le 3$$
- $$a+b \le 15$$

What is the relation with $$x$$ and how do I get the actual result?

In words, what do a, b, c, S1, S2, and S3 represent?

 

[fiksx]

In words, what do a, b, c, S1, S2, and S3 represent?

a,b,c you can see the diagram i drew,
a means PC set include crystal screen and printer
b means PC set include crystal screen and scanner
c mean PC set include scanner and printer 1. $$S_1$$ means 18=a+b+3+crystal screen only
2. $$S_2$$ means 12 = a+c+3+ printer only
3. $$S_3$$ means 6=b+c +3+ scanner only