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

Step-by-step explanation:

Given

$a = \sqrt{f + 4} - \sqrt{36 - f}$

Required

Find f when a  = 4

Substitute 4 for a

$4 = \sqrt{f + 4} - \sqrt{36 - f}$

Rewrite as:

$\sqrt{36 - f} + 4 = \sqrt{f + 4}$

Square both sides

$(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2$

$(\sqrt{36 - f} + 4)^2 = f + 4$

$36 - f + 8\sqrt{36 - f} + 16 = f + 4$

Collect Like Terms

$8\sqrt{36 - f}= f +f+ 4 - 36 -16$

$8\sqrt{36 - f}= 2f -48$

Divide through by 2

$4\sqrt{36 - f}= f -24$

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