Question

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The Shenandoah Valley Cider Farms Company produces apple cider and sells their products to the local retailers. The annual demand for cider is 219,412 gallons. The company is able to produce 292,043 gallons annually. The company is open for 312 days. Annual carrying cost is $0.50 per gallon. The setup cost of production is $512.35. Determine the economic production quantity in gallons. No decimals.

2:

Answer 1

Answer 1:

Let,

D = Annual Demand = 219412 Gallons

N = No. of Days in a Year = 312

u = Daily usage rate = D / N = 219412 / 312 = 703.24 Gallons (Rounded to 2 decimal places)\

p = Daily Production Rate = 292043 / 312 = 936.04 Gallons

O = Ordering or Set Up Cost Per Order = 512.35 $

H = Holding Cost Per Gallon Per Annum = 0.50 $

Then,

EPQ = Optimum Production Quantity = SQRT [ ( 2 X D X O ) / H ] X SQRT [ p / ( p - u ) ] =

= SQRT [ (2 x 219412 x 512.35) / 0.50 ] x SQRT [ 936.04 / (936.04 - 703.24) ]

= SQRT (449662952.8 x 4.02)

= 42521.24 = 42521 Gallons (Rounded to the nearest whole number)