Apencil cup with a capacity of 45 in.3 is to be constructed in the shape of a rectangular box with a square base and an open top. if the material for the sides costs 27¢/in.2 and the material for the base costs 90¢/in.2, what should the dimensions of the cup be to minimize the construction cost?

A 3x3 inches base.

A 3x5 inches sides

Explanation:

As they want the rectangular prism with a square base, you need to make a 3 by 3 base so it is a square and then you just add a 5x3 side to make it 45 in3 and that creates you the minimal cost, because the cheapest would be to make a 1 by 1 but in that one you couldnt fit the pencils efficciently.