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## Sagot :

1.

**Mail Capacity Constraint**:

The distribution center processes up to 150,000 pieces of mail each day.

- Each load by a land carrier can carry 1800 pieces.

- Each load by an air carrier can carry 1500 pieces.

So, if [tex]\( x \)[/tex] represents the number of loads by land carriers and [tex]\( y \)[/tex] represents the number of loads by air carriers, the total number of pieces of mail carried can be represented by the expression [tex]\( 1800x + 1500y \)[/tex].

The center can process a maximum of 150,000 pieces of mail each day, so the inequality representing this constraint is:

[tex]\[ 1800x + 1500y \leq 150,000 \][/tex]

2.

**Load Capacity Constraint**:

The loading equipment can handle a maximum of 150 loads per day. This includes both land and air carriers combined.

Hence, the total number of loads [tex]\( x \)[/tex] (land) plus [tex]\( y \)[/tex] (air) must be less than or equal to 150:

[tex]\[ x + y \leq 150 \][/tex]

Putting these two inequalities together, the system that represents the given situation is:

[tex]\[ 1800x + 1500y \leq 150,000 \][/tex]

[tex]\[ x + y \leq 150 \][/tex]

From the given options, the set of inequalities that matches this is:

[tex]\(1800 x + 1500 y \leq 150,000\)[/tex] and [tex]\(x + y \leq 150\)[/tex].

Thus, the correct choice is the fourth one:

[tex]\[ \boxed{1800 x + 1500 y \leq 150,000 \quad x + y \leq 150} \][/tex]