Problem

Super-Mart has stores in four locations in State A. Super-Mart plans to reapportion its 29 managers based on the number of employees in each store as shown below. Find the standard divisor and each store's standard quota. \begin{tabular}{lccccc} Store & A & B & C & D & Total \\ Number of employees & 80 & 90 & 138 & 248 & 556 \end{tabular} a. What is the standard divisor? The standard divisor is 19.17 . (Round to the nearest hundredth as needed.) b. Find each store's standard quota using the standard divisor from part (a). The standard quota for store $A$ is $\square$. (Round to the nearest hundredth as needed.)

Solution

Step 1 :Given that Super-Mart has 29 managers and 556 employees in total, we can calculate the standard divisor by dividing the total number of managers by the total number of employees.

Step 2 :Using the formula \(\frac{total\_managers}{total\_employees}\), we get \(\frac{29}{556} = 0.052158273381294966\).

Step 3 :Rounding this to the nearest hundredth, we get the standard divisor as \(\boxed{0.05}\).

Step 4 :We can then calculate the standard quota for store A by dividing the number of employees in store A by the standard divisor.

Step 5 :Using the formula \(\frac{store\_A\_employees}{standard\_divisor}\), we get \(\frac{80}{0.05} = 1533.7931034482758\).

Step 6 :Rounding this to the nearest hundredth, we get the standard quota for store A as \(\boxed{1533.79}\).

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