Question

The school band is in charge of a new set of uniforms made with a new logo. A local

business charges $140 to set up the logo with the design and $0.25 in materials per

logo printed. The function C(x) = 140+0.25x / x

represents the average cost per logo if x

uniforms are printed by this business.

a. What is the average cost per uniform to get the logo printed on 25 uniforms?

b. What is the average cost per uniform to get the logo printed on 100 uniforms?

C. How many uniforms should be printed to have an average cost of $1 per logo?

d. What will happen to the price as the number of uniforms printed increases?

Answer 1

Answer:

a. $C(25) = 146.25$

b. $C(100) = 165$

c. $x = 187$

d. Increment in number of uniform causes an increment in price

Step-by-step explanation:

Given

$C(x) = 140 + 0.25x$

Solving (a)

$x = 25$

This gives:

$C(x) = 140 + 0.25x$

$C(25) = 140 + 0.25 * 25$

$C(25) = 140 + 6.25$

$C(25) = 146.25$

Solving (b):

$x = 100$

This gives:

$C(x) = 140 + 0.25x$

$C(100) = 140 + 0.25 * 100$

$C(100) = 140 + 25$

$C(100) = 165$

Solving (c):

Average cost = $1 per logo

For x logos,

Average cost = $1 * x

Average cost = $x

So, we have:

$C(x) = 140 + 0.25x$

$x = 140 + 0.25x$

Collect Like Terms

$x - 0.25x = 140$

$0.75x = 140$

Solve for x

$x = 140/0.75$

$x = 187$ ---- Approximated

Solving (d): What happens when number uniform increases.

Notice that in (a) & (b).

x increases from 25 to 100

Price also increases from $146.25 to $165.

Hence:

Increment in number of uniform causes an increment in price