Northern Distributors is a wholesale organization that supplies retail stores with lawn care and house- hold 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 ware- house can be used to store the Neverfail lawn mow- ers. 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 or- der. 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 ware- house 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. Assume all EOQ conditions are met.

Answer:

Depth added = 80 feet

Cost = $1,740

Step-by-step explanation

Calculation:

Volume of storage warehouse = 60% (width * depth * height)

                                               = 60% (25 * 40 * 8)

                                              = 4,800

Lawn mower's volume = width * depth * height

                                     = 5 * 4 * 2

                                     = 40

Maximum inventory (prior to warehouse expansion) = Volume of storage warehouse / Lawn mower's volume

                                                                                    = 4,800 / 40

                                                                                    = 120 units

Total inventory cost = (Annual demand/qty.) ordering cost/order + (qty./2) carrying cost/order

                                = (12,000/120) * $30 + (120/2) * $2

                                = $3,120

EOQ = [(2*demand*ordering cost/per order) / Carrying cost] ^ (1/2)

        = [(2 * 12,000 * $30) / $2] ^ (1/2)

       = 600

Therefore,

Warehouse required = Lawn mower's volume * EOQ

                            = 40 * 600

                            = 24,000 cu. feet

As per high & width,

Depth = 24,000 cu feet / (25 * 8)

          = 120 feet

Depth added = 120 - 40

                    = 80 feet

Cost after addition:

Volume of storage warehouse = 60% (width * depth * height)

                                               = 60% (25 * 80 * 8)

                                              = 9,600

Lawn mower's volume = width * depth * height

                                     = 5 * 4 * 2

                                     = 40

Maximum inventory (prior to warehouse expansion) = Volume of storage warehouse / Lawn mower's volume

                                                                                    = 9,600 / 40

                                                                                    = 240 units

Total inventory cost = (Annual demand/qty.) ordering cost/order + (qty./2) carrying cost/order

                                = (12,000/240) * $30 + (240/2) * $2

                                = $1,740

Therefore, the firm is willing to pay $1,740.

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