I have no clue how to:
An experimental setup requires a fixed volume of a liquid being stored in a box without a lid. The
four sides of the box must be made of glass to measure the assumed change in colour of that liquid
over time. For safety reasons the base should be made of slate. Slate and glass differ in costs: The
price of slate is r times the price of glass.
1. Minimize the price of the box in terms of r.
2. Assume that the height of the box should not be less than half the width or breadth respectively.
For a box minimized in price this represents a condition on r. Which one?

Question

I have no clue how to:
An experimental setup requires a fixed volume of a liquid being stored in a box without a lid. The
four sides of the box must be made of glass to measure the assumed change in colour of that liquid
over time. For safety reasons the base should be made of slate. Slate and glass differ in costs: The
price of slate is r times the price of glass.
1. Minimize the price of the box in terms of r.
2. Assume that the height of the box should not be less than half the width or breadth respectively.
For a box minimized in price this represents a condition on r. Which one?