Help finding optimal proposal for housing project with a funding limit

There are 2 proposals for a housing project.

x is measured in hundreds of units, and Average Cost(AC) is measured in thousands of dollars

**proposal 1**

**AC1 = x^2 – 4x + 6**

proposal 2

**AC2 = x^3/3 – 3x^2 + 8x + 2**

c) What is the optimal proposal if they can spend no more than $3,000,000?

Using my graphing calculator i found that proposal 1 can build 424 units at an AC of $7017.60 (4.24,7.0176)without going over 30mil and proposal 2 can build 408 at an AC of $7339.90

(4.08,7.339904)

Obviously proposal 1 is better, but how can i show this on paper in proper mathematical format? Help please!!!