Question

SHIPPING A shipping company will ship a package for $7.50 when the volume is no more than 15,000cubiccentimeters. Grace needs to ship a package that is 3⁢𝑥−5 centimeters long, 2⁢𝑥 centimeters wide, and 𝑥+20 centimeters tall.

a. Write a polynomial equation to represent the situation if Grace plans to spend a maximum of $7.50.



___𝑥^3+___𝑥^2+___𝑥= _____

Answer 1

Volume = (3x−5)(2x)(x+20) = 6x^3 + 110x^2 − 200x.
Set equal to the max volume 15,000 cm^3:

6x^3 + 110x^2 − 200x = 15000

(or as an inequality for the "maximum" condition: 6x^3 + 110x^2 − 200x ≤ 15000)

So the blanks: 6x^3 + 110x^2 + (−200)x = 15000.