Question 161581
When {{{C = R}}}, Cost equals Revenue, that is the break-even point. If 
you sell 1 more backpack, you will show the smallest profit possible.
{{{C = 129x + 6687}}}
{{{R = 171x}}}
{{{C = R}}}
{{{129x + 6687 = 171x}}}
Subtract {{{129x}}} from both sides
{{{42x = 6687}}}
{{{x = 159}}} to the nearest whole number
Let Profit = {{{P}}}
{{{P = R - C}}}
I'll find the Profit for 158 backpacks, which should be negative
and for 160 backpacks which should be positive
{{{P = 171x - (129x + 6687)}}}
{{{P = 171x - 129x - 6687}}}
{{{P = 42x - 6687}}}
{{{P[1] = 42*158 - 6687}}}
{{{P[1] = 6636 - 6687}}}
{{{P[1] = -51}}}
{{{P[2] = 42*160 - 6687}}}
{{{P[2] = 6720 - 6687}}}
{{{P[2] = 33}}}
If 160 backpacks are sold, the profit will be $33, the smallest possible