sweetnessnbab
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The revenue from selling \( x \) shirts is \( r(x) = 15x \).

The cost of buying \( x \) shirts is \( c(x) = 7x + 20 \).

The profit from selling \( x \) shirts is \( p(x) = r(x) - c(x) \).

What is \( p(x) \)?

A. \( p(x) = 22x + 20 \)

B. \( p(x) = 22x - 20 \)

C. \( p(x) = 8x + 20 \)

D. [tex]\( p(x) = 8x - 20 \)[/tex]

Sagot :

GinnyAnswer
To determine the profit function \( p(x) \) from selling \( x \) shirts, we must first understand and work with the given expressions for revenue and cost:

1. Revenue Function:
The revenue from selling \( x \) shirts is given by:
[tex]\[ r(x) = 15x \][/tex]

2. Cost Function:
The cost of buying \( x \) shirts is given by:
[tex]\[ c(x) = 7x + 20 \][/tex]

3. Profit Function:
The profit is the revenue minus the cost. Therefore, the profit function \( p(x) \) is defined as:
[tex]\[ p(x) = r(x) - c(x) \][/tex]

Let's substitute the expressions for \( r(x) \) and \( c(x) \) into the profit function:

[tex]\[ p(x) = 15x - (7x + 20) \][/tex]

Next, we need to simplify the expression inside the parentheses:

[tex]\[ p(x) = 15x - 7x - 20 \][/tex]

Subtract \( 7x \) from \( 15x \):

[tex]\[ p(x) = 8x - 20 \][/tex]

So, the profit function \( p(x) \) is:

[tex]\[ p(x) = 8x - 20 \][/tex]

Therefore, the correct answer is:

D. [tex]\( p(x) = 8x - 20 \)[/tex]
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