Question

Business is projected to be booming after the latest release of The Fast and the Furious3.14159265359... Carver's Auto Custom must determine how many cans of paint and rims tostock at their Shanghai location.The Carver Family did choose Warehouse Space A. The warehouse includes 8000 sq. ft. ofshowroom and workshop space. One half of this warehouse space will be used to stock paintcans and rims. The warehouse has a height of 20 ft.Tell how many of rims you will stock. You must have exactly 4 cans ofpaints for every rim you stock.

Answer 1

From the information provided, the warehouse space has 8000 sq ft of showroom and workshop. One hal o this would be used which translates to 4000 sq ft. The warehouse has a height of 20 ft.

The cubic vloume of the warehouse is given as follows;

$\begin{gathered} \text{Vol}=l\times w\times h \\ l\times w=4000,h=20 \\ \text{Vol}=4000\times20 \\ \text{Vol}=80000ft^3 \end{gathered}$

The dimensions for each rim is given as

$\begin{gathered} \text{Dimensions}=36\times36\times15 \\ \text{Note that the dimensions for the rims are measured in inches} \\ 12\text{ inches=1 foot. Therefore,} \\ \text{Dimensions}=3\times3\times1.25 \end{gathered}$

The volume of each rim therefore is;

$\begin{gathered} \text{Vol}=3\times3\times1.25 \\ \text{Vol}=11.25ft^3 \end{gathered}$

To determine how many rims would fit into half of the warehouse,

$\begin{gathered} Number\text{ of rims=}\frac{volume\text{ of warehouse}}{\text{volume of rims}} \\ \text{Number of rims=}\frac{80000}{11.25} \\ \text{Number of rims=}7111.11 \\ \text{Number of rims}\approx7,111 \end{gathered}$

If you must have exactly 4 cans in a rim, then

$\begin{gathered} \text{ Number of cans=Number of rims x 4} \\ \text{ Number of cans=7111 x 4} \\ \text{ Number of cans=28,444} \end{gathered}$