Question 1167856
They will need to buy at least 310-40=270 boxes. They should get a package of 300 boxes at 0.19 a box for a cost of 300x0.19=57, because ordering apackage of 200 and a package of 75 would cost more.
Their total costs depends of the number of boxes. Let's say they sell n boxes.
Their total cost would be 57+250+0.15n if tthey sell n boxes.
The proceds from the sale of those n boxes would be 2.25n.
If 2.25n=57+250+0.15n they are breaking even.
2.25n=57+250+0.15n -> 2.25n-0.15n=57+250 -> 2.10n=307 -> n=307/2.10=146.190467...
They cannot sell that number of boxes, because it is not a wnole number, but if they sell 147 they will turn a small (very small) profit.
As an inequality you would have that to turn a profit, n must be such that
2.25n>57+250+0.15n -> 2.25n-0.15n>57+250 -> 2.10n>307 -> n>307/2.10 n>146.190467...  or n greater than or equal to 147.
with n=147 they collect 2.25x147=330.75 with total costs of
57+250+0.15x147=329.05 . That would be a profit of 330.75-329.05=1.70.