A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie

Question

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.30 per stone for quantities of 600 stones or more, $9.40 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 175 days per year. Usage rate is 25 stones per day and ordering costs are $48. a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Round your intermediate calculations and final answer to the nearest whole number.) Order quantity stones b. If annual carrying costs are 20 percent of unit cost, what is the optimal order size? (Round your intermediate calculations and final answer to the nearest whole number.) Optimal order size stones c. If lead time is 9 working days, at what point should the company reorder? Reorder quantity stones

Explanation / Answer

a. Ordering costs = 8$

Carrying costs = 2$

Demand = usage rate*days per year = 25*175 = 4375 units

EOQ= ((2*Annual Demand*Cost per order)/Holding cost)1/2

= ((2*4375*8)/2)1/2

= 187.08 = 187 units

b. 600 or more

Ordering costs = 8$

Carrying costs = .20*8.3 = 1.66$

Demand = usage rate*days per year = 25*175 = 4375 units

EOQ= ((2*Annual Demand*Cost per order)/Holding cost)1/2

= ((2*4375*8)/1.66)1/2

= 205.35 = 205 units. Not feasible solution

400 to 599

Ordering costs = 8$

Carrying costs = .20*9.4 = 1.88$

Demand = usage rate*days per year = 25*175 = 4375 units

EOQ= ((2*Annual Demand*Cost per order)/Holding cost)1/2

= ((2*4375*8)/1.88)1/2

= 192.96 = 193 units. Not feasible solution

Less than 400

Ordering costs = 10$

Carrying costs = .20*10 = 2$

Demand = usage rate*days per year = 25*175 = 4375 units

EOQ= ((2*Annual Demand*Cost per order)/Holding cost)1/2

= ((2*4375*8)/2)1/2

= 187.08 = 187 units. Feasible solution.

c. Reorder quantitiy= Average daily demand*lead time

= 25*9 = 225 units.

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