College

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



Given:

\[

\begin{align*}

E &= 5q + 40000 \\

q &= -500p + 20000

\end{align*}

\]



Options:

A. \$[/tex]12,000
B. \[tex]$60,000

C. \$[/tex]75,000
D. \$100,000

Answer :

We are given the following equations:

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

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

and the price is given as [tex]$p = 16$[/tex].

Step 1: Find the quantity [tex]$q$[/tex].

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

[tex]$$
q = -500 \times 16 + 20000.
$$[/tex]

Calculate:

[tex]$$
q = -8000 + 20000 = 12000.
$$[/tex]

So, the quantity [tex]$q$[/tex] produced is [tex]$12000$[/tex].

Step 2: Find the expense [tex]$E$[/tex].

Now substitute [tex]$q = 12000$[/tex] into the expense equation:

[tex]$$
E = 5 \times 12000 + 40000.
$$[/tex]

Calculate:

[tex]$$
E = 60000 + 40000 = 100000.
$$[/tex]

Thus, the expense [tex]$E$[/tex] for production when the price is [tex]$\$[/tex]16[tex]$ is $[/tex]\[tex]$\;100,000$[/tex].

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