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The revenue from selling [tex]\(x\)[/tex] shirts is [tex]\(r(x) = 15x\)[/tex].

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

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

What is [tex]\(p(x)\)[/tex]?

A. [tex]\(p(x) = 22x + 20\)[/tex]
B. [tex]\(p(x) = 22x - 20\)[/tex]
C. [tex]\(p(x) = 8x + 20\)[/tex]
D. [tex]\(p(x) = 8x - 20\)[/tex]

Sagot :

GinnyAnswer
To find the profit function [tex]\( p(x) \)[/tex], we need to subtract the cost function [tex]\( c(x) \)[/tex] from the revenue function [tex]\( r(x) \)[/tex].

Given:
[tex]\[ r(x) = 15x \][/tex]
[tex]\[ c(x) = 7x + 20 \][/tex]

The profit function [tex]\( p(x) \)[/tex] is calculated as follows:
[tex]\[ p(x) = r(x) - c(x) \][/tex]

Substitute the given functions for [tex]\( r(x) \)[/tex] and [tex]\( c(x) \)[/tex]:
[tex]\[ p(x) = 15x - (7x + 20) \][/tex]

Distribute the negative sign:
[tex]\[ p(x) = 15x - 7x - 20 \][/tex]

Combine like terms:
[tex]\[ p(x) = (15x - 7x) - 20 \][/tex]
[tex]\[ p(x) = 8x - 20 \][/tex]

Thus, the profit function [tex]\( p(x) \)[/tex] is:
[tex]\[ p(x) = 8x - 20 \][/tex]

Therefore, the correct answer is:
D. [tex]\( p(x) = 8x - 20 \)[/tex]
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