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A clothing design company pays two different people to design its T-shirts.
The company pays person A $10 an hour and pays person B $12. Person A
cannot work more than 5 more hours than person B, but they cannot work
more than 30 hours total. Person A makes the company a profit of $15 an
hour, and person B makes the company a profit of $20 an hour. If the
company wants to make at least $250 in profit, which value will minimize the
cost to the company? (Each point is (a, b), where a is the hours person A
works and b is the hours person B works.)
A. (0, 12.5)
B. (17.5, 12.5)
C. (10, 20)
D. (0,30)
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Answer :

AI-generated answer

To find the value that will minimize the cost to the company while ensuring a profit of at least $250, we can set up the following constraints and objective function:

Let x be the hours person A works and y be the hours person B works. The constraints are:

1. $10x + $12y ≤ $30 (total hours cannot exceed 30)

2. x ≤ y + 5 (person A cannot work more than 5 more hours than person B)

The profit function can be expressed as:

Profit = $15x + $20y

Now, we want to maximize the profit while meeting the constraints. However, the question asks for the minimum cost to the company, which is the cost of labor. Since the cost of labor is $10x + $12y, we need to minimize this cost.

To solve this problem, we can graph the feasible region based on the constraints and then find the point within the region that minimizes the cost.

Upon solving the equations, we get the following feasible region:

A. (0, 12.5)

B. (17.5, 12.5)

C. (10, 20)

D. (0,30)

To minimize the cost, we need to find the point that minimizes $10x + $12y while ensuring a profit of at least $250. We need to substitute the values of x and y into the cost function and find the point that satisfies the conditions.

The correct answer that minimizes the cost to the company while ensuring a profit of at least $250 is:

B. (17.5, 12.5)Answer:

Step-by-step explanation: Yeah I explained in the answer^^^^^^^^^^^^^^

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