Chapter 12.2, Problem 26PPS

To determine

The best buy size of popcorn by using the ratio of the cost to the volume of the popercorn size.

Use the following data table:

Popcorn sizes available
Size	Length   $\left(in\right)$	Width   $\left(in\right)$	Height   $\left(in\right)$	Price   $\left(\$\right)$
Small	$5$	$4$	$8$	$4.50$
Medium	$7$	$5$	$10$	$5.75$
Large	$10$	$6$	$12$	$6.50$

Answer to Problem 26PPS

The large size of the popcorn bag is best buy.

Explanation of Solution

Given:

Popcorn sizes available
Size	Length   $\left(in\right)$	Width   $\left(in\right)$	Height   $\left(in\right)$	Price   $\left(\$\right)$
Small	$l_s=5$	$w_s=4$	$h_s=8$	$P_s=4.50$
Medium	$l_M=7$	$w_M=5$	$h_M=10$	$P_M=5.75$
Large	$l_L=10$	$w_L=6$	$h_L=12$	$P_L=6.50$

Concept Used:

The volume of the rectangular prism is given by the following expression:

  $V=l\times w\times h$

Where,

Length of rectangular prism: $l$

Width of rectangular prism: $w$

Height of rectangular prism: $h$

Calculation:

In the given eg:

There are three sizes are available for the popcorn as small, medium and large.

Let’s take volume for each size:

Volume of small size popcorn:

  $\begin{array}{l}{V}_s=l_s\times w_s\times h_s\\ V_s=5\times 4\times 8\\ V_s=160i{n}^3\end{array}$

Volume of medium size popcorn:

  $\begin{array}{l}{V}_m=l_m\times w_m\times h_m\\ V_m=7\times 5\times 10\\ V_m=350i{n}^3\end{array}$

Volume of large size popcorn:

  $\begin{array}{l}{V}_L=l_L\times w_L\times h_L\\ V_L{}_s=5\times 4\times 8\\ V_L{}_s=720i{n}^3\end{array}$

Take the ratio of the cost to volume of each poprcorn bag size:

  $\begin{array}{l}S=\frac{P_s}{V_s}=\frac{4.50}{160}=0.028125\\ M=\frac{P_M}{V_M}=\frac{5.75}{350}=0.01642\\ L=\frac{P_L}{V_L}=\frac{6.50}{720}=9.027\times {10}^{-3}=0.009027\end{array}$

So, the large size of the popcorn bag is best buy as it has low ratio value of the cost and its volume.

Conclusion:

Hence, the large size of the popcorn bag is best buy.