Question

A rectangular box is going to be made with a volume of $274c{m}^3.$ The base of the box will be a square and the top will be open. The cost of the material for the base is $0\mathrm{.}3$ cents per square centimeter, and the cost of the material for the sides is $0\mathrm{.}1$ cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it$.$ What is the minimum cost?

Select the correct answer below:

$$0\mathrm{.}29$

$$0\mathrm{.}33$

$$0\mathrm{.}42$

$$0\mathrm{.}47$