The demand for motorcycle tires imported by Dixie Import-Export is 43,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $430, and the cost of storing each tire for a year is $2. Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)
Annual demand R43000 Ordering cost O$430 per order Carrying cost C$2 per year per unit. Optimal order quantity Q Sqrt{2OR/C} Sqrt{2*430*43000/2} 4,300tires T Q/R 4300/430 10 orders have to be placed per year. ** Is it? Then what is the correct answer?
Let x be the optimal number of tires in shipment. Total number of shipments will be 43,000/x Shipment costs number of shipments*430 43,000/x*430 The stock of tires will start at x and uniformly decrease to 0 until the next shipment, so on average, there will be x/2 tires in the stock Storage costs x/2*2 x Total cost (c) 43,000*430/x + x Take the derivative of this and solve for c'0 c' -18,490,000/x^2 + 1 0 x^2 18,490,000 x 4300
Annual demand R43000 Ordering cost O$430 per order Carrying cost C$2 per year per unit. Optimal order quantity Q Sqrt{2OR/C} Sqrt{2*430*43000/2} 4,300tires T Q/R 4300/430 10 orders have to be placed per year. ** Is it? Then what is the correct answer?
Let x be the optimal number of tires in shipment. Total number of shipments will be 43,000/x Shipment costs number of shipments*430 43,000/x*430 The stock of tires will start at x and uniformly decrease to 0 until the next shipment, so on average, there will be x/2 tires in the stock Storage costs x/2*2 x Total cost (c) 43,000*430/x + x Take the derivative of this and solve for c'0 c' -18,490,000/x^2 + 1 0 x^2 18,490,000 x 4300
