Final answer:
Option C is the correct set of inequalities representing the scenario where Greg designs shorts and T-shirts with constraints on production time and daily item quotas. The correct option being C. s ≥ 12-t, s ≤ 28-t, 0.5t + 0.66s ≤ 18; s ≥ 0; t ≥ 0.
Step-by-step explanation:
The student is asking about a set of inequalities that represent the scenario of Greg owning a clothing store and designing pairs of shorts and T-shirts with certain constraints related to price, time, and quantity. We need to establish inequality expressions that consider the time he can work and the minimum and maximum items he must create daily.
Considering the time Greg can work, which is 15 hours a day, and the time it takes to design each type of clothing,
- It takes Greg 0.5 hours to design a T-shirt (t).
- It takes Greg 1.5 hours to design a pair of shorts (s).
- Greg can work for a maximum of 15 hours daily.
The inequality to represent the time constraint is 0.5t + 1.5s ≤ 15, which after dividing all terms by 0.5 simplifies to t + 3s ≤ 30.
As for the constraints on the number of items, Greg has to design at least 10 items daily and cannot design more than 25 items in one day. Therefore, we have the inequalities 10 ≤ t + s and t + s ≤ 25.
Since both s and t must be non-negative, we also include s ≥ 0 and t ≥ 0.
Combining all constraints, the set of inequalities that represents the scenario is:
C. s ≥ 12-t, s ≤ 28-t, 0.5t + 0.66s ≤ 18; s ≥ 0; t ≥ 0
This is the correct option that represents Greg's situation. The mention of the sale prices for shorts and T-shirts sets the context but does not affect the constraints related to time and quantity for item design.