Questions: Peter Bell of Bell Electronics maintains an extensive stock of computer components for the consumer market. He has hundreds of drawers/cabinets for the many small parts (mother boards, graphic cards, fans, etc.), and he wants to organize them so as to minimize his travel and maximize his time at the counter interacting with customers. ITEM WEEKLY TRIPS AREA NEEDED (DRAWERS) A 319 29 B 296 4 C 230 5 D 32 16 E 72 6 a) Which item should be stored at the very front (closest to the counter)? Fill in the table below for the ratios of the number of trips to drawers of storage area (enter your responses as whole numbers). ITEM TRIPS/DRAWERS A B C D E should be stored at the very front (closest to the counter). b) Which item should be stored at the very back (furthest from the counter)? should be stored at the very back (furthest from the counter).

Peter Bell of Bell Electronics maintains an extensive stock of computer components for the consumer market. He has hundreds of drawers/cabinets for the many small parts (mother boards, graphic cards, fans, etc.), and he wants to organize them so as to minimize his travel and maximize his time at the counter interacting with customers.

ITEM  WEEKLY TRIPS  AREA NEEDED (DRAWERS) 
A  319  29 
B  296  4 
C  230  5 
D  32  16 
E  72  6 

a) Which item should be stored at the very front (closest to the counter)?

Fill in the table below for the ratios of the number of trips to drawers of storage area (enter your responses as whole numbers).

ITEM  TRIPS/DRAWERS 
A  
B  
C  
D  
E  

 should be stored at the very front (closest to the counter).

b) Which item should be stored at the very back (furthest from the counter)?

 should be stored at the very back (furthest from the counter).
Transcript text: Peter Bell of Bell Electronics maintains an extensive stock of computer components for the consumer market. He has hundreds of drawers/cabinets for the many small parts (mother boards, graphic cards, fans, etc.), and he wants to organize them so as to minimize his travel and maximize his time at the counter interacting with customers. \begin{tabular}{ccc} \hline ITEM & WEEKLY TRIPS & AREA NEEDED (DRAWERS) \\ \hline A & 319 & 29 \\ B & 296 & 4 \\ C & 230 & 5 \\ D & 32 & 16 \\ E & 72 & 6 \\ \hline \end{tabular} a) Which item should be stored at the very front (closest to the counter)? Fill in the table below for the ratios of the number of trips to drawers of storage area (enter your responses as whole numbers). \begin{tabular}{cc} \hline ITEM & TRIPS/DRAWERS \\ \hline A & $\square$ \\ B & $\square$ \\ C & $\square$ \\ D & $\square$ \\ E & $\square$ \\ \hline \end{tabular} $\square$ should be stored at the very front (closest to the counter). b) Which item should be stored at the very back (furthest from the counter)? $\square$ should be stored at the very back (furthest from the counter).
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Solution

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Solution Steps

To determine which item should be stored closest to the counter, we need to calculate the ratio of the number of weekly trips to the number of drawers needed for each item. The item with the highest ratio should be stored at the very front. Conversely, the item with the lowest ratio should be stored at the very back.

Step 1: Calculate the Ratios

We calculate the ratio of weekly trips to the area needed in drawers for each item as follows:

\[ \text{Ratio} = \frac{\text{Weekly Trips}}{\text{Drawers}} \]

The calculated ratios are:

  • For item A: \( \frac{319}{29} = 11 \)
  • For item B: \( \frac{296}{4} = 74 \)
  • For item C: \( \frac{230}{5} = 46 \)
  • For item D: \( \frac{32}{16} = 2 \)
  • For item E: \( \frac{72}{6} = 12 \)
Step 2: Identify the Closest and Furthest Items

From the calculated ratios, we identify:

  • The item with the highest ratio (closest to the counter) is item B with a ratio of 74.
  • The item with the lowest ratio (furthest from the counter) is item D with a ratio of 2.

Final Answer

The item that should be stored at the very front (closest to the counter) is \( \boxed{B} \) and the item that should be stored at the very back (furthest from the counter) is \( \boxed{D} \).

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