Question

Greg owns a clothing store where he designs T-shirts, t, and pairs of shorts, s. He sells the T-shirts for $7 each and the shorts for $16. Greg can work 18 hours a day, at most. It takes him 30 minutes to design a T-shirt and 45 minutes to design a pair of shorts. He must design at least 12 items each day, but he cannot design more than 28 items in one day. Which set of inequalities below represents this scenario?

A. s ≥ 12 - t, s ≤ 28 - t, 0.5s ≥ 18 - 0.66t, s ≥ 0, t ≥ 0
B. s ≥ 12 - t, s ≥ 28 - t, s ≤ 24 - 0.66t, s ≥ 0, t ≥ 0
C. s ≥ 12 - t, s ≤ 28 - t, 0.5t + 0.66s ≤ 18, s ≥ 0, t ≥ 0
D. s ≥ 12 + t, s ≤ 28 + t, s ≤ 24 - 0.66t, s ≥ 0, t ≥ 0

Answer 1

The correct set of inequalities representing the scenario involving Greg's clothing store is option C. It takes into account the time it takes to design T-shirts and shorts, the maximum work hours, and the minimum and maximum number of items Greg must design per day.

Step-by-step explanation:

The set of inequalities that represents Greg's clothing store scenario involving designing T-shirts, t, and shorts, s, is C: s ≥ 12 - t, s ≤ 28 - t, 0.5t + 0.75s ≤ 18, s ≥ 0, t ≥ 0. Let's break down the constraints:

• Each T-shirt takes 30 minutes (0.5 hours) and each pair of shorts takes 45 minutes (0.75 hours) to design. Greg can work at most 18 hours a day: 0.5t + 0.75s ≤ 18.
• He must design at least 12 items a day: t + s ≥ 12, which is equivalent to s ≥ 12 - t.
• He cannot design more than 28 items a day: t + s ≤ 28, or s ≤ 28 - t.
• The quantities of T-shirts and shorts designed must be non-negative: t ≥ 0 and s ≥ 0.