# Thread: Help finding optimal proposal for housing project with a funding limit

1. ## 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!!! 2. Originally Posted by seanP 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!!!
Substitute $AC = 3\,000\,000$ into each equation and solve each for $x$.