M7_IND4. Andre Greipel is the owner of a small company that produces heart rate monitors. The annual demand is for 2,250 heart rate monitors, and Andre produces these devices in batches. On average, Andre can produce 140 monitors per day during the production process. Demand for monitors has been about 35 monitors per day. The cost to set up the production process is $350, and it costs Andre $0.80 to carry 1 monitor in inventory for one year. How many monitors should Andre produce in each batch

Answer :

a) Economic Production Quantity = 1,612 monitors

b) Number of setups = 1.4

c) Total cost = $972.12 per year

Explanation :

As per the data given in the question,

a) Economic Production Quantity = sqrt((2 × annual demand × set up cost) ÷ carrying cost × (1 - daily demand ÷ daily production))

=sqrt((2 × 2,250 × $350) ÷ $0.80 × (1 - 35 ÷ 140))

= 1,620.19

= 1,621 monitors

b) Number of setups = Annual demand ÷ Economic production quantity

= 2,250 ÷ 1,621

= 1.3880

= 1.4

c) Formula of Total cost = Carrying cost + Annual setup cost

Carrying cost=(Economic production quantity ÷ 2) × Carrying cost × (1 - daily demand ÷ daily production)

= (1,612 ÷ 2)× $0.80 × (1 -35 ÷ 140)

= $486.30

Annual setup cost = (Annual demand ÷ Economic production quantity) × setup cost

= (2,250 ÷ 1,621) × $350

= $485.812

So, Total cost = $486.30 + $485.812

= $972.12 each year

We simply applied the above formulas

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