A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price...

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A jewelry firm buys semiprecious stones to make bracelets andrings. The supplier quotes a price of $8.00 per stone forquantities of 600 stones or more, $8.30 per stone for orders of 400to 599 stones, and $10 per stone for lesser quantities. The jewelryfirm operates 175 days per year. Usage rate is 25 stones per day,and ordering costs are $48. a. If carrying costs are $2 per yearfor each stone, find the order quantity that will minimize totalannual cost. (Round your intermediate calculations and final answerto the nearest whole number.) Order quantity stones b. If annualcarrying costs are 30 percent of unit cost, what is the optimalorder size? (Round your intermediate calculations and final answerto the nearest whole number.) Optimal order size stones c. If leadtime is 10 working days, at what point should the company reorder?Reorder quantity stones

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4.1 Ratings (867 Votes)

This is a problem where the economic order quantity Q needs tobe calculated Lets start from the basicsLet P be the unit cost and D be the annual demand quantityThe purchase cost will be PDSuppose we order Q items Then the number of orders we wouldplace would be DQ per year If the fixed cost per order is K thenthe total ordering cost could be DKQThe average inventory can be assumed to be Q2 as the inventoryvaries between Q and 0 Suppose the annual holding cost per unit ish Then the holding or inventory cost would be Qh2Summing up we getTotal Cost TC PD DKQ Qh2 Formula 1If the function TC were differentiable then one could take thederivative of the function set it to zero and then compute theoptimal Q QLets do that Total Cost TC PD DKQ Qh2Differentiation wrt Q we get0 DKQ2 h20or DKQ2 h2Q2 2DKhQsqrt2DKh Formula 2This is a neat little formula Unfortunately in our case thefunction is not smooth because the value of P changes with thevalue of Q So how do we work on this problemLet us go back one step and examine the derivative whichdescribes See Answer

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