Question

A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 4 apparel items will be manufactured, how many units of fabric should be ordered?

Answer 1

Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Explanation:

Given

`a = √(f + 4) - √(36 - f)`

Required

Find f when a = 4

Substitute 4 for a

`4 = √(f + 4) - √(36 - f)`

Rewrite as:

`√(36 - f) + 4 = √(f + 4)`

Square both sides

`(√(36 - f) + 4)^2 = (√(f + 4))^2`

`(√(36 - f) + 4)^2 = f + 4`

`36 - f + 8√(36 - f) + 16 = f + 4`

Collect Like Terms

`8√(36 - f)= f +f+ 4 - 36 -16`

`8√(36 - f)= 2f -48`

Divide through by 2

`4√(36 - f)= f -24`

Square both sides

`16(36-f) = (f - 24)^2`

`16(36-f) = f^2 - 48f + 576`

`576-16f = f^2 - 48f + 576`

`-16f = f^2 - 48f`

Collect like terms

`f^2 - 48f + 16f = 0`

`f^2 -32f = 0`

Factorize

`f(f - 32) = 0`

`f = 0` or
`f = 32`

f can not be 0 because some units must be ordered.

So, f = 32