Q square root formula range 3 1805788 range 4 2013468

Q* (Square root formula)
Range 3
1805.788
Range 4
2013.468
Order Quantity 1805.788 5000
Holding cost $415.33 $925.00
Setup cost $415.33 $150.00
Unit costs $23 , 000 . 00 $18 , 500 . 00
Total cost, T
c
$23,830.66 $19,575.00
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
148. A local artisan uses supplies purchased from an overseas supplier. The owner believes the
assumptions of the EOQ model are met reasonably well. Minimization of inventory costs is her
objective. Relevant data, from the files of the craft firm, are annual demand (D) =150 units,
ordering cost (S) = $42 per order, and holding cost (H) = $4 per unit per year
a. How many should she order at one time?
b. How many times per year will she replenish her inventory of this material?
c. What will be the total annual inventory costs associated with this material?
d. If she discovered that the carrying cost had been overstated, and was in reality only $1 per unit
per year, what is the corrected value of EOQ?
a.
Q
*
=
b.
N =
2 ⋅ 150 ⋅ 42
= 56.12
. She should order 56 units at a time.
4
150
= 2.67
She should place about 2.67 orders per year.
56.12
c. The inventory costs are $112 for holding and $112 for ordering, or $224 total.
d. At the lower value for H, the EOQ will be doubled to 112.25.
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}

149. The annual demand for an item is 40,000 units. The cost to process an order is $40 and the annual
inventory holding cost is $3 per item per year. What is the optimal order quantity, given the
following price breaks for purchasing the item?
Quantity Price
1-1,499 $2.50 per unit
1,500 - 4,999 $2.30 per unit
5,000 or more $2.25 per unit
a. What is the optimal behavior?
b. Does the firm take advantage of the lowest price available? Explain.
a. Purchase 1500 units at a time, paying $2.30 each.
b. It is not advantageous to pay $2.25 if that requires ordering 5000 units. The annual cost is
$97,820.00 at the $2.25 price versus $95,316.67 annual cost at the $2.30 price.
Q* (Square root formula)
Range 1
1032.796
Range 2
1032.796
Range 3
1032.796
Order Quantity 1032.796 1500 5000
Holding cost $1,549.19 $2,250.00 $7,500.00
Setup cost $1,549.19 $1,066.67 $320.00
Unit costs $100,000.00 $92,000.00 $90,000.00
Total cost, T
c
$103,098.39 $95,316.67 $97,820.00
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
150. Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying
costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an
order. Assume the basic EOQ model with no shortages applies. Assume 52 weeks per year, closed
on Mondays.
a. How many pounds should Groundz order at a time?
b. What is total annual cost (excluding item cost) of managing this item on a cost-minimizing
basis?
c. In pursuing lowest annual total cost, how many orders should Groundz place annually?
d. How many days will there be between orders (assume 310 operating days) if Groundz practices
EOQ behavior?
a.
Q
*
=
2 ⋅ 4 ⋅ 52 ⋅ 8
= 8
. Groundz should order 8 pounds per order.
1 ⋅ 52
b.
TC =
4 ⋅ 52
⋅ 8 +
8
⋅ 1 ⋅ 52 = 208 + 208 = 416
. The firm will spend $416 annually.