Question

hi can you help me solve this problem?AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost of $50,000 and a production cost of $7 for each timer manufactured. The timers sell for $13 each.(a) What is the cost function C(x)?C(x) = (b) What is the revenue function R(x)?R(x) = (c) What is the profit function P(x)?P(x) = (d) Compute the profit (loss) corresponding to production levels of 3000, 7000, and 10,000 timers, respectively. (Input a negative value to indicate a loss.)3000 timers $7000 timers $10,000 timers $

Answer 1

Let:

x = Number of timers

The function cost is given by:

$C(x)=50000+7x$

The revenue cost is given by:

$R(x)=13x$

The profit is given by:

$\begin{gathered} P(x)=R(x)-C(x) \\ P(x)=13x-(50000+7x) \\ P(x)=6x-50000 \end{gathered}$

(d)

x = 3000

$\begin{gathered} P(3000)=6(3000)-50000 \\ P(3000)=-32000 \end{gathered}$

x = 7000

$\begin{gathered} P(7000)=6(7000)-50000 \\ P(7000)=-8000 \end{gathered}$

x = 10000

$\begin{gathered} P(10000)=6(10000)-50000 \\ P(10000)=10000 \end{gathered}$