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The monthly rent for a pizza parlor is [tex]$1,200. The average production cost per pizza is $[/tex]6.75. The monthly expenses for the pizza parlor are given by the function [tex]$E(x) = 1,200 + 6.75x$[/tex], where [tex]$x$[/tex] is the number of pizzas sold. For [tex]$x$[/tex] pizzas sold, the pizza parlor's revenue is given by the function [tex]$R(x) = 12.5x$[/tex].

The monthly profit of the pizza parlor is the difference between its revenue and its expenses. Which function represents the monthly profit, [tex]$P(x)$[/tex]?

A. [tex]$P(x) = 5.75x + 1,200$[/tex]
B. [tex]$P(x) = 5.75x - 1,200$[/tex]
C. [tex]$P(x) = 1,200 + 19.25x$[/tex]
D. [tex]$P(x) = 6.25x - 1,200$[/tex]

Sagot :

GinnyAnswer
To determine which function represents the monthly profit [tex]\( P(x) \)[/tex] of the pizza parlor, we need to understand that profit is the difference between revenue and expenses. Given the provided information:

- The monthly rent is \[tex]$1,200. - The average production cost per pizza is \$[/tex]6.75.
- The monthly expenses are given by the function [tex]\( E(x) = 1,200 + 6.75x \)[/tex], where [tex]\( x \)[/tex] is the number of pizzas sold.
- The revenue for [tex]\( x \)[/tex] pizzas sold is given by the function [tex]\( R(x) = 12.5x \)[/tex].

The profit function [tex]\( P(x) \)[/tex] is calculated as follows:

[tex]\[ P(x) = R(x) - E(x) \][/tex]

Substituting the given functions for revenue and expenses:

[tex]\[ P(x) = 12.5x - (1,200 + 6.75x) \][/tex]

Simplify the expression:

[tex]\[ P(x) = 12.5x - 1,200 - 6.75x \][/tex]

Combine like terms:

[tex]\[ P(x) = (12.5x - 6.75x) - 1,200 \][/tex]
[tex]\[ P(x) = 5.75x - 1,200 \][/tex]

Therefore, the monthly profit function [tex]\( P(x) \)[/tex] is:

[tex]\[ P(x) = 5.75x - 1,200 \][/tex]

From the given options, the correct answer is:

B. [tex]\( P(x) = 5.75x - 1,200 \)[/tex]
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