document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184583>Question 1184583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $ 0.50 per kg of milk plus a $20 delivery fee (the $ 20 fee is independent of the amount ordered; i.e., $20 is the order cost). Bruno's holding cost is $ 0.03 per kg per month. He needs 9000 kg of milk per month.\r<BR>\n" );
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document.write( "Note: (if your obtained values are NOT an integer, please round to Nearest 10th; otherwise it does not match the answer).\r<BR>\n" );
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document.write( "Suppose Bruno orders 9000 kg each time.  His average inventory is <BR>\n" );
document.write( "4500<BR>\n" );
document.write( "   kg. <BR>\n" );
document.write( "Suppose Bruno orders 7000 kg each time. He will place <BR>\n" );
document.write( "15.43<BR>\n" );
document.write( " orders with his supplier each year.<BR>\n" );
document.write( " To minimize the sum of the ordering and holding costs, Bruno should order <BR>\n" );
document.write( "3464.10<BR>\n" );
document.write( " kg from his supplier with each order. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849839 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down Bruno's gelato milk ordering costs and find the optimal order quantity.\r<BR>\n" );
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document.write( "**1. Current Scenario (9000 kg orders):**\r<BR>\n" );
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document.write( "* **Annual Demand:** 9000 kg/month * 12 months/year = 108,000 kg/year<BR>\n" );
document.write( "* **Order Quantity:** 9000 kg<BR>\n" );
document.write( "* **Number of Orders per Year:** 108,000 kg / 9000 kg/order = 12 orders/year<BR>\n" );
document.write( "* **Average Inventory:** 9000 kg / 2 = 4500 kg (as stated)<BR>\n" );
document.write( "* **Annual Holding Cost:** 4500 kg * $0.03/kg/month * 12 months/year = $1620<BR>\n" );
document.write( "* **Annual Ordering Cost:** 12 orders * $20/order = $240<BR>\n" );
document.write( "* **Annual Purchase Cost:** 108,000 kg * $0.50/kg = $54,000<BR>\n" );
document.write( "* **Total Annual Cost:** $1620 + $240 + $54,000 = $55,860\r<BR>\n" );
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document.write( "**2. Scenario with 7000 kg orders:**\r<BR>\n" );
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document.write( "* **Order Quantity:** 7000 kg<BR>\n" );
document.write( "* **Number of Orders per Year:** 108,000 kg / 7000 kg/order ≈ 15.43 orders/year (as stated)<BR>\n" );
document.write( "* **Average Inventory:** 7000 kg / 2 = 3500 kg<BR>\n" );
document.write( "* **Annual Holding Cost:** 3500 kg * $0.03/kg/month * 12 months/year = $1260<BR>\n" );
document.write( "* **Annual Ordering Cost:** 15.43 orders * $20/order ≈ $308.60<BR>\n" );
document.write( "* **Annual Purchase Cost:** 108,000kg * $0.50/kg = $54,000<BR>\n" );
document.write( "* **Total Annual Cost:** $1260 + $308.60 + $54,000 = $55,568.60\r<BR>\n" );
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document.write( "**3. Economic Order Quantity (EOQ):**\r<BR>\n" );
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document.write( "The EOQ formula minimizes the total ordering and holding costs. It's given by:\r<BR>\n" );
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document.write( "EOQ = √(2 * D * S / H)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* D = Annual demand (108,000 kg)<BR>\n" );
document.write( "* S = Ordering cost ($20)<BR>\n" );
document.write( "* H = Annual holding cost per unit ($0.03/kg/month * 12 months/year = $0.36/kg/year)\r<BR>\n" );
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document.write( "EOQ = √(2 * 108,000 kg * $20 / $0.36/kg)<BR>\n" );
document.write( "EOQ = √(4,320,000 / 0.36)<BR>\n" );
document.write( "EOQ = √12,000,000<BR>\n" );
document.write( "EOQ ≈ 3464.10 kg (as stated)\r<BR>\n" );
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document.write( "**4. Optimal Ordering Cost and Holding Cost:**\r<BR>\n" );
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document.write( "With the EOQ, the annual holding cost and the annual ordering cost are roughly equal.\r<BR>\n" );
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document.write( "* **Annual Holding Cost:** (3464.10 kg / 2) * $0.36/kg = $623.54<BR>\n" );
document.write( "* **Annual Ordering Cost:** (108,000 kg / 3464.10 kg) * $20 = $623.54<BR>\n" );
document.write( "* **Annual Purchase Cost:** 108,000kg * $0.50/kg = $54,000<BR>\n" );
document.write( "* **Total Annual Cost:** $623.54 + $623.54 + $54,000 = $55,247.08\r<BR>\n" );
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document.write( "**Conclusion:**\r<BR>\n" );
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document.write( "Bruno should order approximately 3464.10 kg of milk per order to minimize his total costs. This will result in approximately 31.2 orders per year.<BR>\n" );
document.write( " </SPAN>\n" );
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