College

Determine the expense, [tex]\( E \)[/tex], for the production of an item when the price [tex]\( p \)[/tex] is [tex] \$16 [/tex]. Given:

\[
\begin{array}{l}
E = 5q + 40000 \\
q = -500p + 20000
\end{array}
\]

A. [tex] \$12,000 [/tex]
B. [tex] \$60,000 [/tex]
C. [tex] \$75,000 [/tex]
D. [tex] \$100,000 [/tex]

Answer :

Given the price [tex]$p = 16$[/tex], we first find the production quantity [tex]$q$[/tex] using the equation

[tex]$$
q = -500p + 20000.
$$[/tex]

Substitute [tex]$p = 16$[/tex] into the equation:

[tex]$$
q = -500(16) + 20000 = -8000 + 20000 = 12000.
$$[/tex]

Now, we calculate the expense [tex]$E$[/tex] using the formula

[tex]$$
E = 5q + 40000.
$$[/tex]

Substitute [tex]$q = 12000$[/tex] into this equation:

[tex]$$
E = 5(12000) + 40000 = 60000 + 40000 = 100000.
$$[/tex]

Thus, the expense for production when the price is [tex]$\$[/tex]16[tex]$ is

$[/tex][tex]$
\boxed{100000}.
$[/tex]$

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