Thread: 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!!!

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 into each equation and solve each for .