Answer:
The company would save $10.5
Step-by-step explanation:
First, we have to remember that the total surface area of a rectangular box is:
[tex]A=2lh+2wh+2lw[/tex]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:
[tex]\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}[/tex]BOX 2:
[tex]\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}[/tex]Now, let's convert each surface area into square foot:
[tex]\begin{gathered} A_1=448in^2*\left(\frac{1ft}{12in}\right)^2\rightarrow A_1=\frac{28}{9}ft^2 \\ \\ A_2=424in^2*\left(\frac{1ft}{12in}\right)^2\rightarrow A_2=\frac{53}{18}ft^2 \end{gathered}[/tex]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:
[tex]A_1=\frac{28}{9}ft^2\rightarrow\frac{28}{9}ft^2*\frac{1.25\text{ }USD}{ft^2}\rightarrow3.89\text{ USD}[/tex][tex]A_2=\frac{53}{18}ft^2\rightarrow\frac{53}{18}ft^2*\frac{1.25\text{ }USD}{ft^2}\rightarrow3.68\text{ USD}[/tex]Now we multiply this individual cost by 50 to get the cost of 50 boxes of each type:
[tex]B_1=3.89*50=194.5[/tex][tex]B_2=3.68*50=184[/tex]Now, we find the difference between both prices:
[tex]194.5-184=10.5[/tex]This way, we can conlcude that the company would save $10.5
