Solving an equation. Please help

Question

The daily cost for baking x loaves of bread at Joanna’s bakery is given in dollars by C=0.3+ square root 5x + 4000. If bread at Joanna’s bakery sells for $1.00 a loaf,how many loaves must Joanna sell to make profit?

Answer 1

Given C= .3 + SQRT(5x+4000) and each loaf sells for $1

1x > .3 + SQRT(5x+4000). Because she makes $1 per loaf

(X-.3) = SQRT(5x+4000).  Square both sided

(X-.3)^2 = (SQRT(5x+4000))^2

X^2 - .6x + .09 = 5x + 4000

X^2 - 5.6x -3999.91

The negative root is not feasible so the positive root 66 is the only possible root. 

Answer 2

Price of x loaves is x*1.00 = x dollars.

Joana makes profit when x > 0.3 + √(5x+4000)

=> (x-0.3) > √(5x+4000)

=> (x-0.3)² > 5x+4000

=> x² -.6x +0.09 > 5x+4000

=>x² -5.6x -3999.91 > 0

Now roots of x² -5.6x -3999.91=0 are 66.1 and -60.5

For the inequality to be true, we need:

x > 66.1 and x>-60.5 or x <66.1 and x <-60.5

i.e x > 66.1 or x <-60.5

x being number if loaves, x is always >0.

Hence minimum of laves is 67.

Crosscheck: .Cost =3 + √(5*67+4000) = 66.14 < 67=Selling Price, i.e Profitable