Math Snap

STEP 1

Assumptions1. The weekly fixed costs are $7000. The average cost per clock for the business to manufacture$x$clocks is described by the function$\frac{0.4x +7000}{x}$
3. We need to find the average cost when $x=100,1000$, and $10,000$

STEP 2

First, let's find the average cost when $x=100$. We can do this by substituting $x=100$ into the given function.
$$Average\, cost = \frac{0.4 \times100 +7000}{100}$$

STEP 3

Calculate the average cost when $x=100$.
Average\, cost = \frac{40 +7000}{100} = \($\)70.40

STEP 4

Next, let's find the average cost when $x=1000$. We can do this by substituting $x=1000$ into the given function.
$$Average\, cost = \frac{0.4 \times1000 +7000}{1000}$$

STEP 5

Calculate the average cost when $x=1000$.
Average\, cost = \frac{400 +7000}{1000} = \($\)7.40

STEP 6

Finally, let's find the average cost when $x=10,000$. We can do this by substituting $x=10,000$ into the given function.
$$Average\, cost = \frac{0.4 \times10,000 +7000}{10,000}$$

Calculate the average cost when $x=10,000$.
Average\, cost = \frac{4000 +7000}{10,000} = \($\)1.10The average cost when manufacturing100 clocks is $70.40 per clock, when manufacturing1000 clocks it's$7.40 per clock, and when manufacturing10,000 clocks it's $1.10 per clock.