Given are following : Annual demand = D = 6000 widgets/year Ordering cost = Co =
ID: 373735 • Letter: G
Question
Given are following :
Annual demand = D = 6000 widgets/year
Ordering cost = Co = $75
Annual unit holding cost = Ch = 30% of purchase price
Thus,
Optimum order quantity , Q
= Square root ( 2 x Co x D /Ch)
= Square root ( 2 x 75 x 6000/Ch)
= Square root ( 900000/Ch)
Answer to question 57:
Ch for 1 – 999 range = 30% of 0.90 = $0.27
Therefore , Q = Square root ( 900000/0.27) = 1825.74 ( 1826 rounded to nearest whole number )
Q VALUE = 1826
Answer to question 58:
Ch for 1000 – 2999 range = 30% of $0.88 = $0.264
Therefore , Q = Square root ( 900000/0.264) = 1846.37 ( 1846 rounded to nearest whole number )
Q VALUE = 1846
Answer to question 59 :
Ch for 3000 + category = 30% of $0.86 = $ 0.258
Therefore, Q = square root ( 900000/0.258) = 1867.71 ( 1868 rounded to nearest whole number )
Answers to question 60, 61 and 62 :
Since , 1826 is outside the quantity range 1 – 999, feasible Q value = 999
Since, 1846 Is within the quantity range 1000 – 2999, feasible Q value = 1846
Since 1868 is outside quantity range of 3000+_, feasible Q value = 3000
Answer to question 63 :
Total cost
= Annual purchase cost + Annual ordering cost + annual inventory holding cost
= Purchase price/ unit x Annual demand + Ordering cost x Number of orders + annual unit inventory cost x Average inventory
= Purchase price/unit x 6000 + Cox Annual demand/feasible order quantity + Ch x Order quantity /2
= 0.90 x 6000 + 75 x 6000/999 + 0.27 x 999/2
= 5400 + 450.45 + 134.86
= $ 5985.31
Answer to question 64 :
Total cost
= Annual purchase cost + Annual ordering cost + annual inventory holding cost
= Purchase price/ unit x Annual demand + Ordering cost x Number of orders + Annual unit inventory cost x Average inventory
= Purchase price/unit x 6000 + Cox Annual demand/feasible order quantity + Ch x Order quantity /2
= 0.88 x 6000 + 75 x 6000/1846 + $0.264 x 1846/2
= 5280 + 243.77 + 243.67
= $ 5767.54
Answer to question 65 :
Total cost
= Annual purchase cost + Annual ordering cost + annual inventory holding cost
= Purchase price/ unit x Annual demand + Ordering cost x Number of orders + Annual unit inventory cost x Average inventory
= Purchase price/unit x 6000 + Cox Annual demand/feasible order quantity + Ch x Order quantity /2
= 0.86 x 6000 + 75 x 6000/3000 + 0.258 x 6000/2
= 5160 + 150 + 774
= $6084
Answer to question 66:
Order quantity that minimizes cost = 1846
Q VALUE = 1826
Explanation / Answer
A company uses 6,000 widgets a year. Order costs are $75 and carrying costs are 30 percent of the purchase price. The price breakdown is as follows:
1 - 999 $0.90
1,000 – 2,9999 $0.88
3,000+ $0.86
Calculate the order quantity and use that information to answer the questions that follow.
57.) What is the Q value for the 1 – 999 price category before it is adjusted for feasibility?
Round your answer to a whole number.
58.) What is the Q value for the 1,000 – 2,999 price category before it is adjusted for feasibility?
Round your answers to a whole number.
59.) What is the Q value for the 3,000+ price category before it is adjusted for feasibility?
Round your answers to a whole number.
60.) What is the feasible Q value for the 1 – 999 price category? Round your answer to a whole number.
61.) What is the feasible Q value for the 1,000 – 2,999 price category? Round your answer to a whole number.
62.) What is the feasible Q value for the 3,000+ price category? Round your answer to a whole number.
63.) What is the total cost for the 1 – 999 price category? Round your answer to a whole number.
64.) What is the total cost for the 1,000 – 2,999 price category? Round your answer to a whole number.
65.) What is the total cost for the 3,000+ price category? Round your answer to a whole number.
66.) Based on your calculations, what is the order quantity that minimizes cost?
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