Question

Gillian can spend up to $300 buying both cotton shirts and wool shirts for her club. The cotton shirts cost $15 each and the wool shirts cost $20 each. The number of wool shirts Gillian will buy will be at least 3, and no more than half the number of cotton shirts she buys.

The graph shows the feasible region, where x represents the number of cotton shirts and y represents the number of wool shirts.


Which ordered pairs meet all the constraints and make sense in context of the situation?

Select each correct answer.



Responses

(11,4)
begin ordered pair 11 comma 4 end ordered pair

(13, 4)
begin ordered pair 13 comma 4 end ordered pair

(6, 2)
begin ordered pair 6 comma 2 end ordered pair

(12,5)
begin ordered pair 12 comma 5 end ordered pair

(16, 4)
beign ordered pair 16 comma 4 end ordered pair

Answer 1

I could really use some help solving this question. My brain just isn't working today.

Answer 2

The problem states that there is a graph available of the feasible region, so in order to find the point(s) that satisfy the constraints you simply need to see which answer choices are within the feasible region.

Answer 3

Since Gillian can spend up to $300 and the cotton shirts cost $15 each and the wool shirts cost $20 each, we can set up the following constraints:

1. The cost of cotton shirts (15x) plus the cost of wool shirts (20y) must be less than or equal to $300.
Mathematically, this constraint can be written as: 15x + 20y ≤ 300.

2. The number of wool shirts (y) must be at least 3.
Mathematically, this constraint can be written as: y ≥ 3.

3. The number of wool shirts (y) must be no more than half the number of cotton shirts (x).
Mathematically, this constraint can be written as: y ≤ 0.5x.

Now, let's look at the graph to determine which ordered pairs meet all these constraints. Without the graph, I can't see the exact shape and location of the feasible region, but I can provide some general observations.

The feasible region is the area on the graph that satisfies all the given constraints. To find the ordered pairs that meet these constraints, you would look for points within or on the boundary of this region.

Here's what we can infer based on the constraints:

- The number of wool shirts (y) must be at least 3, so any point with y < 3 is not valid.

- The number of wool shirts (y) must be no more than half the number of cotton shirts (x), so as you move to the right on the graph (increasing x), y must not increase too quickly.

- The total cost (15x + 20y) must not exceed $300.

You would need to examine the graph to see which ordered pairs satisfy all these conditions. If you have access to the graph, please look for the points within the feasible region, and those points would be the ordered pairs that meet all the constraints and make sense in the context of the situation.