A tailor makes shirts and dresses. It takes 6 hours to make a shirt and 4 hours to make a dress. The tailor spends at least 240 hours. The labour cost of making a shirt is Sh. 60 and that of a dress i

A tailor spends 6 hours to make a shirt and 4 hours to make a dress. The tailor takes at least 240 hours.
Total time: $6x + 4y$.
"At least 240 hours" means greater than or equal to 240.

$$6x + 4y \ge 240$$

Divide by 2 to simplify:

$$\boxed{3x + 2y \ge 120}$$

The labour cost of making a shirt is Sh. 60 and that of a dress is Sh. 70. The total labour cost should not exceed Sh. 4,200.
Total labour cost: $60x + 70y$.
"Should not exceed Sh. 4,200" means less than or equal to 4,200.

$$60x + 70y \le 4200$$

Divide by 10 to simplify:

$$\boxed{6x + 7y \le 420}$$

The tailor must make at least 20 shirts.
"At least 20 shirts" means greater than or equal to 20.

$$\boxed{x \ge 20}$$

The tailor must make more than 16 dresses.
"More than 16 dresses" means strictly greater than 16.

$$\boxed{y > 16}$$

The four inequalities are:

1. $3x + 2y \ge 120$
2. $6x + 7y \le 420$
3. $x \ge 20$
4. $y > 16$