Question

Acme Logistics provides "Less than truck load" (LTL) services throughout the U.S. They have several hubs where they use cross-docking to move goods from one trailer to another. Acme built its last hub 10 years ago, and it had 36 dock doors. The cost index at that time was 140, and the total cost was $6 million. Acme plans a new hub that will have 48 dock doors. The cost index now is 195, and Acme will use a capacity factor of 0.82. What is the estimated cost of the new hub?

Answer 1

Answer:

The answer is "$10.12 million"

Explanation:

To find the price of the 36 dock doors only at the current rate, just use the cost index.  

$C_n=C_k \times (\frac{I_n}{I_k})$

     $= 6 \times \frac{195}{140} \\\\= \ \ 8 \ million$

Its current cost of 36 dock doors is, thus,$\ \ 8 \ million$. To calculate the price for 48 dock doors, just use the second formula now:

$\to (\frac{C_A}{C_B})=(\frac{S_A}{S_B})^{X}\\\\\to C_A=C_B \times (\frac{S_A}{S_B})^{X}$

         $=8 \times (\frac{48}{36})^{0.82}\\\\= \ 10.12 \ million$