Ajewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 30 cm3. if nickel plating costs $1 per cm2 and silver plating costs $3 per cm2, find the dimensions of the box to minimize the cost of the materials

The dimension of the box to minimize the cost of the materials is

According to the question, the volume of the jewelry box is .

Let the dimension of the base of the jewelry box be and the height be  . So,

------------eq

It has sides,

So, the Cost of the sides

As the box has square base so top and bottom so, the cost of nickel plating is

Now,

From eq ,

Minimum cost is evaluated as,

Simplify further-

Hence, the dimension of the box to minimize the cost of the materials is

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u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w