Question

Northern Distributors is a wholesale organization that supplies retail stores with lawn care and household products. One building is used to store Neverfail lawn mowers. The building is 25 feet wide by 40 feet deep by 8 feet high. Anna Oldham, manager of the warehouse, estimates that about 60% of the warehouse can be used to store the Neverfail lawn mowers. The remaining 40% is used for walkways and a small office. Each Neverfail lawn mower comes in a box that is 5 feet by 4 feet by 2 feet high. The annual demand for these lawn mowers is 12,000, and the ordering cost for Northern Distributors is $30 per order. It is estimated that it costs Northern $2 per lawn mower per year for storage. Northern Distributors is thinking about increasing the size of the warehouse. The company can do this only by making the warehouse deeper. At the present time, the warehouse is 40 feet deep. How many feet of depth should be added onto the warehouse to minimize the annual inventory costs? How much should the company be willing to pay for this addition? Remember that only 60% of the total area can be used to store Neverfail lawn mowers. (Show all work)

Answer 1

Volume of the building = 25*40*8 = 8000 Cubic feet

60% can be used for storage of Lawn mower = 60% of 8000 = 4,800 Cu Feet

Volume of Lawnmower = 5*4*2 = 40 Cu Feet

No. of lawnmowers that can be stored = (4800/40) = 120

EOQ of lawn mowers = Square root of (2*12000*30)/2 = 600

Total Order cost = (12000/600)*30 = $600

Given that order and storage cost are same at EOQ, total cost = 600*2 = $1,200

Storage and ordering cost when only 120 units can be stored

Ordering = (12000/120)*30 = $3000

Storage = (120/2)*2 = $120.............. Total cost of $3,120

Thus, by ordering at EOQ company can save 3,120 - 1200 = $1,920 in a year.

To store 600 lawnmowers, space required would be 600*40 Cu feet = 24,000 Cu ft

24,000 Cu Ft is 60% of building, hence building need to be (24,000/60%) = 40,000 Cu ft

Let the height be X, then 25*X*8 = 40,000

X = 200

The height of the building needs to be 200ft (Additional 160 ft), for this the company would be willing to pay $1,920