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A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Grace needs to ship a package that is 3x-5 centimeters long, 2x centimeters wide, and x + 20 centimeters tall. A.Write a polynomial expression to represent the situation if Grace plan as to spend a maximum of $7.50
B. Write and solve a system of equations
C. What should the dimensions of the package be to have the maximum volume?

Respuesta :

raphealnwobi

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

What is an inequality?

An inequality is an expression that shows the non equal comparison between two or more numbers and variables.

A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Hence, if Grace plan as to spend a maximum of $7.50:

Volume (V) = (3x - 5)(2x)(x + 20) = 6x³ + 110x² - 200x

The inequality is:

6x³ + 110x² - 200x ≤ 15000

6x³ + 110x² - 200x - 15000 ≤ 0

x = 10

The maximum volume is at:

V' = 0

V' = 18x² + 220x - 200 = 0

x = 0.85 cm

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

Find out more on inequality at: https://brainly.com/question/24372553

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