Use what you learned back in algebra for this sort ofquadratic word problems:

[html]+-----------+--------------+-----------+--------------------+-----------+

| number of | resulting | number | total | total |

| increases | price | sold | income | costs |

+-----------+--------------+-----------+--------------------+-----------+

| 0 | $400 | 50 | (50)(400) | (50)(120) |

+-----------+--------------+-----------+--------------------+-----------+

| 1 | $400 - 1($5) | 50 + 1(1) | (50 + 1)(400 - 5) | (51)(120) |

+-----------+--------------+-----------+--------------------+-----------+

| 2 | $400 - 2($5) | 50 + 2(1) | (50 + 2)(400 - 10) | (52)(120) |

+-----------+--------------+-----------+--------------------+-----------+

| ... | | | | |

+-----------+--------------+-----------+--------------------+-----------+

| x | | | | |

+-----------+--------------+-----------+--------------------+-----------+[/html]

Keep going (in the "..." part) until you see the pattern. Then plug "x" into that pattern to create your "total income" and "total costs" expressions. Subtract to find the "profit" expression.

Then use what you learned back in algebra aboutgraphing quadratics(specifically, that the max/min point is given by the vertex) to find the solution.

If you get stuck, please reply showing how far you have gotten. Thank you!