Question

The Friendly Sausage Factory (FSF) can produce hot dogs at a rate of 5,250 per day. FSF supplies hot dogs to local restaurants at a steady rate of 250 per day. The cost to prepare the equipment for producing hot dogs is $65. Annual holding costs are 45 cents per hot dog. The factory operates 295 days a year. a. Find the optimal run size. (Do not round intermediate calculations. Round your answer to the nearest whole number.) b. Find the number of runs per year. (Round your answer to the nearest whole number.) c. Find the length (in days) of a run

Answer 1

Answer:

a.

4,730 units

b.

16 production runs

c.

1 day

Explanation:

a.

Use the following formula to calculate the optimal run size

Optimal run size = Economic production quantity = $\sqrt{\frac{2 D S }{H} }$ x $\sqrt{\frac{p}{p - d}}$

Where

D = Annual Demand = Daily demand x Numbers operating days = 250 x 295 days = 73,750

S = Ordering cost = $65

H = Holding cost = $0.45 per unit

p = Daily production = 5,250 per day

d = daily dmand = 250 per day

Placing values in the formula

Optimal run size = $\sqrt{\frac{2 X 73,750 X 65 } {0.45} }$ x $\sqrt{\frac{5,250}{5,250 - 250}}$

Optimal run size = 4,615.79 x 1.0246951 = 4,729.77 = 4,730 units

b.

Numbers of production run = Demand / Optimal run size = 73,750 / 4,730 = 15.5919 production runs = 16 production runs

c.

Length (in days) of a run = Optimal run size / Daiy production = 4,730 / 5,250 = 0.901 days  = 0.90 days = 1 days