Question

The material used to make a storage box costs $1.25 per square foot. The boxes have the same volume. How much does a company save by choosing to make 50 of box 2 instead of 50 of Box 1? Question 15

Answer 1

The company would save $10.5

Explanation:

First, we have to remember that the total surface area of a rectangular box is:

`A=2lh+2wh+2lw`

Where:

• l, is the ,lenght, of the box

,

• w, is the ,width, of the box

,

• h ,is the ,height, of the box

Now, let's calculate the total surface area of each one of the boxes:

BOX 1:

`\begin{gathered} A_1=2\left(20\right)\left(4\right)+2\left(6\right)\left(4\right)+2\left(20\right)\left(6\right) \\ \rightarrow A_1=448in^2 \end{gathered}`

BOX 2:

`\begin{gathered} A_2=2\left(15\right)\left(8\right)+2\left(4\right)\left(8\right)+2\left(15\right)\left(4\right) \\ \rightarrow A_2=424in^2 \end{gathered}`

Now, let's convert each surface area into square foot:

`\begin{gathered} A_1=448in^2*\left((1ft)/(12in)\right)^2\rightarrow A_1=(28)/(9)ft^2 \\ \\ A_2=424in^2*\left((1ft)/(12in)\right)^2\rightarrow A_2=(53)/(18)ft^2 \end{gathered}`

Now, we multiply each surface area by the cost of the material per square feet to find the cost of one unit of each box:

`A_1=(28)/(9)ft^2\rightarrow(28)/(9)ft^2*\frac{1.25\text{ }USD}{ft^2}\rightarrow3.89\text{ USD}`
`A_2=(53)/(18)ft^2\rightarrow(53)/(18)ft^2*\frac{1.25\text{ }USD}{ft^2}\rightarrow3.68\text{ USD}`

Now we multiply this individual cost by 50 to get the cost of 50 boxes of each type:

`B_1=3.89*50=194.5`
`B_2=3.68*50=184`

Now, we find the difference between both prices:

`194.5-184=10.5`

This way, we can conlcude that the company would save $10.5