Answer:
- Base Length = 7.368cm
- Height = 0.737cm.
Step-by-step explanation:
Volume of the jewelry box=
The box has a square base and is to be built with silver plated sides and nickel plated top and base.
Therefore: Volume = Square Base Area X Height = l²h
Total Surface Area of a Cuboid =2(lb+lh+bh)
Since we have a square base
Total Surface Area =
The Total Surface Area of the box
Nickel plating costs $1 per
Silver Plating costs $10 per
Since the sides are to be silver plated and the top and bottom nickel plated:
Therefore, Cost of the Material for the jewelry box
Recall earlier that we derived:
Substituting into the formula for the Total Cost
The minimum costs for the material occurs at the point where the derivative equals zero.
Recall:
The box which minimizes the cost of materials has a square base of side length 7.368cm and a height of 0.737cm.