McDuff Preserves expects to bottle and sell 3,000,000 32oz.jars of jam. The comp
ID: 3092248 • Letter: M
Question
McDuff Preserves expects to bottle and sell 3,000,000 32oz.jars of jam. The company orders its containers fromConsolidated Bottle Company. The cost of ordering a shipmentof bottles is $300, and the cost of storing each empty bottle for ayear is $.60. How many orders should McDuff place per year and howmany bottles should be in each shipment if the ordering and storagecosts are to be minimized? (Assume that each shipment of bottles isused up before the next shipment arrives). Pleas round answer tonearest natural number. I'm so lost McDuff Preserves expects to bottle and sell 3,000,000 32oz.jars of jam. The company orders its containers fromConsolidated Bottle Company. The cost of ordering a shipmentof bottles is $300, and the cost of storing each empty bottle for ayear is $.60. How many orders should McDuff place per year and howmany bottles should be in each shipment if the ordering and storagecosts are to be minimized? (Assume that each shipment of bottles isused up before the next shipment arrives). Pleas round answer tonearest natural number. I'm so lostExplanation / Answer
Somewhere, in the middle, is a lowest cost operatingpoint.
Let's write an equation of cost:
Varirables are number per order, N.
Note that storage time is N/3E6 - That assumes the 3millionjars is per year - not really stated but needed.
The average storage amount is N/2 which is a linear ramp fromN to zero during each order period. - Average is 1/2 the startvalue.
Cost per bottle is constant, and will be ignored, as 3E6bottles are always going to be bought per year.
Number of orders per year is 3E6/N, which is 1/storage timewhich is N/3E6
So, cost, which needs to be minimized, is as follows:
C = 300 * 3E6/N + .6 * N/2
We need to take the derivative of this d/dN and set to zero tofind the minimum
0 = -900E6/N2 + .3 : .3N2 = 900E6 : N2 = 3E9 : N =54,772