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Q1 (Total 20 points)

Based on the information provided in the problem description, we know that the production rate p=5000 units/day, the demand rate d=250 units/day, the fixed cost for each production run/cycle S=$22, and the holding cost rate H=$0.15/unit/year. As the factory operates 300 days, hence D=d*300=75000units/year.

1) The optimal total production quantity per cycle is

Q=[pic]=[pic]4812.265 units.

The corresponding maximal on-hand stock level is Q*(1-d/p)=4812.265*(1-250/5000) =4571.652 units.

2) The optimal number of cycles per year is D/Q=15.59.

3) The optimal length of each cycle is Q/D=0.064years or 19.25 days.

Q2 (Total 30 points)

Based on the problem description, here is the summary of the quantity discount scheme:

|Range of Quantity |Price |Holding Cost Rate ($/year/unit) |

| |($/unit) | |

|0 – 999 |5 |2 |

|1000 - 3999 |4.95 |1.98 |

|4000 – 5999 |4.9 |1.96 |

|6000 more |4.85 |1.94 |

Also note that the fixed cost per order S= $50 and the annual demand rate D =4900 units.

Let us check the lowest purchase price of 4.85, the corresponding EOQ quantity is

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It is not feasible, and we need to check the next lowest purchase price of 4.9.

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Again, it is not feasible. The next purchase price is 4.95 and the corresponding EOQ quantity is

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It is still not feasible, the next purchase price is 5 and the corresponding EOQ quantity is

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This one is feasible. In order to choose the overall optimal order quantity, we need to compare the total average cost...