Question

Math 112 Written Homework: Polynomial Functions Student Name: Instructor S.Andrews 1. A packa perimeter of the ging company will only accept packages for shipment if the sum of its height and base is not more than 260 inches. Write a function to represent ight and perimeter the volume of a box with a square base, with sum of the he of the base equal to 260 inches. Label the provided diagram with your variables. What dimensions of such a box will give the maximum volume? Show how you found this. DO NOT USE A DERIVATIVE (if you do, the entire homework will receive a 0). What is the maximum volume? Use a sentence and specify units.
ASAP PLEASE!

Answer 1

Given The sum of the height f perimeter is equal to 260 lets base is square of side = a height = h sum of the height & perimeter is equal to 260 4 a + h = 260 h = 260 - 4a (where perimeter of a square = 4a) volume (v) = a^2 h V = a^2 (260 - 4a) V = 260 a^2 - 4a^3 (a) For maximum volume dv/da = 0 d/da (260a^2 - 4a^3) = 0 260 times 2a - 4 times 3a^2 = 0 \r\n 520 a - 12a^2 = 0 12a = 520 a = 520/12 a = 43.333 inch h = 260 - 4a = 260 - 4 times 43.333 h = 86.6667 inch a = 43.333 inch and h = 86.6667 inch will give the maximum volume. (b) The maximum volume v_max = 260 times (43.333)^2 - 4 (43.333)^3 v_max = 162740.7407 inch.