Jon owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.

He sells shorts for $14 and T-shirts for $6 each. Jon can work 12 hours a day,

at most. It takes him 15 minutes to design a T-shirt and an hour to design a

pair of shorts. He must design at least 12 items each day, but he cannot

design more than 20 items in one day. Which set of inequalities below

represents this scenario?

The set of inequalities representing the scenario are:

Price = 14 s + 6 t

Time: s + 0.15 t ≤ 12

Number of items: 12 ≤ s + t ≤ 20.

Step-by-step explanation:

The clothes designed by Jon is denoted as follows:

s = shorts

t = T-shirt

The cost of the items are:

Cost of shorts = $14

Cost of T-shirt = $6

Determine the price function:

Price = 14 s + 6 t

It is provided that Jon can work 12 hours a day, at most. Also it takes him 15 minutes to design a T-shirt and an hour to design a pair of shorts.

The time function is as follows:

Time: s + 0.15 t ≤ 12

It is also provided that Jon must design at least 12 items each day. But he cannot design more than 20 items in one day.

The number of items designed each day is given by the inequality:

Number of items:

s + t ≥ 12

s + t ≤ 20

⇒ 12 ≤ s + t ≤ 20.