Ergonomics Inc. sells ergonomically designed office chairs. The company has the
ID: 420666 • Letter: E
Question
Ergonomics Inc. sells ergonomically designed office chairs. The company has the following information:
Average demand = 26 units per day
Average lead time = 52 days
Item unit cost = $72 for orders of less than 420 units
Item unit cost = $69 for orders of 420 units or more
Ordering cost = $47
Inventory carrying cost = 25%
The business year is 250 days
Assume there is no uncertainty at all about the demand or the lead time.
a. Calculate EOQ if unit cost is $72 and $69. (Note: These EOQs do not need to be feasible in their price range.) (Round up your answers to the next whole number.)
EOQ at $72 = ___
EOQ at $69= ___
b. Calculate annual ordering costs for each alternative? (Round your answers to 2 decimal places.)
annual ordering cost at $72 = ___
annual ordering cost at $69= ___
c. Calculate annual inventory carrying costs for each alternative? (Round your answers to 2 decimal places.)
annual inventory carrying costs at $72 = ___
annual inventory carrying costs at $69= ___
d. Calculate annual product costs for each alternative?
annual product costs at $72 = ___
annual product costs at $69= ___
e. What will be the total costs for each alternative? (Round your answers to 2 decimal places.)
total costs at $72= ___
total costs at $69= ___
f. Based on your analysis, how many chairs should they order at a time? (Round your answers to 2 decimal places.)
g. How much the firm can save annually by using the order quantity in Part f. instead of the first EOQ shown in Part a? (Round your answer to 2 decimal places.)
Explanation / Answer
Following are to be noted :
Annual demand = D = 26 units/ day x 250 days = 6500
Ordering cost = Co = $47
Annual unit inventory holding cost =Ch = 25% of unit inventory cost
Accordingly Ch1 = 25% of $72 ( for orders less than 420 units ) = $18
Ch2 = 25% of $69 ( for orders more than or equal to 420 ) = $17.25
EOQ can be formulated as =Square root ( 2 x Co x D/ Ch )
Answer to question a :
Therefore .
EOQ at $72 = Square root ( 2 x Co x D / Ch1 ) = Square root ( 2 x 47 x 6500/18)= 184.24 ( 185 rounded to next whole number )
EOQ at $69 = Square root ( 2 x Co x D / Ch2) = Square root ( 2 x 47 x 6500/17.25) = 188.20 ( 189 rounded to next higher whole number )
Answer to question b :
Annual ordering cost
= Ordering cost x Number of orders
= Ordering cost x annual demand / EOQ
= Co x D/EOQ
Therefore ,
Annual ordering cost at $72
= $47 x 6500/ 185
= $1651.35
Annual ordering cost at $69
= $47 x 6500/ 189
= $1616.40
Answer to question c :
Annual inventory carrying cost
= annual unit inventory carrying cost x Average inventory
= Ch x EOQ/ 2
Therefore ,
Annual inventory carrying cost at $72 =$18 x 185/ 2 = $1665
Annual inventory carrying cost at $69 = $17.25 x 189/2 = $1630.12
Answer to question d :
Annual product cost at $72 = $72 x 6500 = $468000
Annual product cost at $69 = $69 x 6500 = $448500
Answer to question e :
Total cost = Annual ordering cost + annual inventory carrying cost + Annual product cost
Total cost at $72 = $1651.35 + $1665 + $468000 = $471316.35
Total cost at $69 = $1616.40 + $1630.12 + $448500 = $451746.52
Answer to question f :
Since total cost at $69 is less , the corresponding EOQ which is189 should be ordered t a time
Answer to question g :
Amount the firm can save annually
= $471316.35 - $451746.52
= $19569.83
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