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The Deer Valley Farm (DVF) produces a natural organic fertilizer, which it sells mostly to gardeners and homeowners. The annual demand for fertilizer is 220,000 pounds. The farm is able to produce 305,000 pounds annually. The cost to transport the fertilizer to from the plant to the farm is $620 per load. The DVF sells the fertilizer in containers with 40 pounds of fertilizer. The annual carrying cost is 0.12 per pound.
a. Compute the optimum load size, the maximum fertilizer level at the farm, and the total minimum cost.
b. If the farm can increase the production capacity to 360,000 pounds per year, will it reduce total inventory costs?

Sagot :

Anthougoidn

Answer:

The Deer Valley Farm (DVF)

a. Optimum load size = 7,625 containers

Maximum fertilizer level at the farm = 5,500 containers

Total minimum cost = $189,110,200

b. No.  Total inventory costs will increase.

Explanation:

a) Data and Calculations:

Annual demand for fertilizer = 220,000 pounds

Annual production units = 305,000 pounds

Inventory = 85,000 pounds

Cost to transport the fertilizer to and from the plant to the farm = $620

Each container holds = 40 pounds

Annual carrying cost per pound = $0.12

Optimum load size = 305,000/40 = 7,625 containers

Maximum fertilizer level at the farm = 5,500 containers (220,000/40)

Total minimum cost = $ ($620 * 305,000) + ($0.12 * 85,000)

= $189,110,200 ($189,100,000 + 10,200)

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