The Metropolitan Book Company purchases paper from the Atlantic Paper Company 200 miles away. Metropolitan produces paperbacks that require 1,215,000 yards of paper per year. The cost per order is $1200; the cost of holding 1 yard of paper in inventory is $0.09 per year. 1. What is the minimum total annual inventory cost

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Answer:

The answer is "162,000"

Explanation:

Annual Request of paper annually  D =  $ 1 215,000  

Cost per order S = $ 1200  

Cost of keeping H = $.09 a year

quantity of the  economic order (EQ) = [tex]\sqrt{ \frac{(2\times D \times S)}{H}}[/tex]

                                                    [tex]=\sqrt{ \frac{(2\times 1,215,000 \times 1,200)}{0.09}}\\\\= \frac{54000}{0.3}\\\\=180,000[/tex]

 Minimum total annual cost = [tex]\frac{D \times S }{(EQ)} + H \times \frac{(EQ)}{2}[/tex]

                                              [tex]= \frac{1,215,000 \times 1200}{ 180,000} + \frac{ 0.09 \times 180,000}{ 2}\\\\= \frac{1,215,00 \times 12}{ 18} + 0.09 \times 90,000\\\\= \frac{1,458,000}{ 18} + 0.09 \times 90,000\\\\=81,000 + 81,000\\\\=162,000[/tex]