A rectangular container is open at the top and must have a volume of 10 yards^3.

Question

A rectangular container is open at the top and must have a volume of 10 yards^3.See figure below. The side materials cost C dollars per square yard, while material for the bottom cost 2C dollars per quare yard.

a. Solve for the optimal dimensions using Langrane multipliers

b. What are the units for lamda1.

c. It it were desired to have the container hold 13 yards^3 instead of 10yards^3, by how much would cost be expected to increase? Use the value of lamda1 to estimate the change in cost. Do not resolve the problem

A rectangular container is open at the top and must have a volume of 10 yards^3.See figure below. The side materials cost C dollars per square yard, while material for the bottom cost 2C dollars per quare yard. Solve for the optimal dimensions using Langrane multipliers What are the units for lambda1. It it were desired to have the container hold 13 yards^3 instead of 10yards^3, by how much would cost be expected to increase? Use the value of lambda1 to estimate the change in cost. Do not resolve the problem

Explanation / Answer

Since this is a rectangular container, we see that:

V = LWH.

Since L = 2W, we see that:

V = (2W)WH
==> V = 2W

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