(a) Calculate the economic order quantity (EOQ):
The economic order quantity (EOQ) formula is given by:
EOQ = sqrt((2 * D * S) / H)
Where:
D = Annual demand = 300 units
S = Ordering cost = $5
H = Annual holding cost = 20% of the unit cost
To calculate the EOQ, we need to determine the unit cost based on the given price
ranges.
For quantities 1-80: Cost per item = $20
For quantities 81-200: Cost per item = $18
For quantities 201 and above: Cost per item = $16
Since the annual demand is 300 units, we need to consider the price range for
quantities 201 and above.
Unit cost = $16
Holding cost = 20% of $16 = $3.2
Plugging these values into the EOQ formula:
EOQ = sqrt((2 * 300 * 5) / 3.2)
= sqrt(3000 / 3.2)
= sqrt(937.5)
≈ 30.64
Therefore, the economic order quantity (EOQ) is approximately 30.64 units.
(b) How many times per year does the store reorder at feasible order quantity?
To determine the number of times the store reorders at the feasible order quantity,
we need to calculate the reorder frequency using the following formula:
Reorder frequency = (Annual demand) / (EOQ)
Reorder frequency = 300 / 30.64
≈ 9.8
Therefore, the store reorders at the feasible order quantity approximately 9.8 times
per year. Since this is not a whole number, we can assume the store would reorder
9 times per year.
(c) What is the total annual cost if the EOQ is ordered?
To calculate the total annual cost if the EOQ is ordered, we need to consider the
following costs:
Ordering cost:
Ordering cost per order = Ordering cost * Reorder frequency
= $5 * 9
= $45
Holding cost:
Holding cost per year = (EOQ / 2) * Holding cost
= (30.64 / 2) * $3.2
= 15.32 * $3.2
≈ $49.06
Total annual cost = Ordering cost + Holding cost
= $45 + $49.06
≈ $94.06
The total annual cost if the EOQ is ordered is approximately $94.06.
(d) What is the total annual cost if the order quantity falls in other price ranges?
For quantities 1-80: Cost per item = $20
Unit cost = $20
Holding cost = 20% of $20 = $4
Total annual cost = Ordering cost + Holding cost
= $45 + (EOQ/2) * Holding cost
= $45 + (30.64/2) * $4
= $45 + 61.28
= $106.28
(e) Explanation and suggestions to the store:
Based on the analysis above, the economic order quantity (EOQ) for the pharmacy
is approximately 30.64 units. The store reorders at the feasible order quantity
approximately 9 times per year. If the EOQ is ordered, the total annual cost would
be approximately $106.28, regardless of the price range.