A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a priceof $8 per stone for quantities of 600 stones or more, $9 per stone for orders of 400 to 599 stones,and $10 per stone for lesser quantities. The jewelry firm operates 200 days per year. Usage rate is25 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 totalannual cost.b. If annual carrying costs are 30 percent of unit cost, what is the optimal order size?c. If lead time is six working days, at what point should the company reorder?

Question
Asked Mar 5, 2020
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A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price
of $8 per stone for quantities of 600 stones or more, $9 per stone for orders of 400 to 599 stones,
and $10 per stone for lesser quantities. The jewelry firm operates 200 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.
b. If annual carrying costs are 30 percent of unit cost, what is the optimal order size?
c. If lead time is six working days, at what point should the company reorder?

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Expert Answer

Step 1

A jewelry firm buys semiprecious stones to make bracelets and rings

600(or more) $8/stone

400 to 599       $9/stone

399(or less) $10/stone

N = 200 days/year

d = 25 stones/ day

s = $48

Operations Management homework question answer, step 1, image 1

Step 2

A)

If carrying costs are$2 per year for each stone, the order quantity that will minimize total annual cost

 

Operations Management homework question answer, step 2, image 1

Step 3

This is the in-quantity range of 400-599 units.

Now, we should calculate the total cost of 490 units ad the total cost of breakeven point 600 units.

Operations Management homework question answer, step 3, image 1

...

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