A company would like to build a new manufacturing facility and has selected thre

Question

A company would like to build a new manufacturing facility and has selected three potential locations The cost information about each location is shown below Location B, Yearty fixed cost $970,000, Unit variable cost $85 Location Ci Yearly fixed cost $1,150,000, Unit variable cost $60 Location D: Yearly fixed cost = $850,000: Unit variable cost-$110, Do NOT use any comma in your answer When necessary, use at least 4 decimal places in your calculation and answer The crossover quantity between location B and location D is The crossover quantity between location B and location C is units units If the quantity is betweenand units, then location D is the most economical site However, location C has the lowest fotal cost for any quantity above units

Explanation / Answer

Crossover quantity is the quantity for which total costs for two locations are identical.

Let the crossover quantity between location B and D is N1

Total cost for location B for quantity N1 = $970,000 + 85.N1

Total cost for location D for quantity N1 = $850,000 + 110.N1

Therefore ,

970,000 + 85.N1 = 850,000 + 110.N1

Or, 110.N1 – 85.N1 = 970,000 – 850,000

Or, 25.N1 = 120,000

Or, N1 = 120,000/25

Or, N1 = 4800

Let the crossover quantity between location B and location C = N2

Total cost for location B = $970,000 + 85.N2

Total cost for location C = $1150,000 + 60.N2

Therefore ,

970,000 + 85.N2 = 1150,000 + 60.N2

Or, 25.N2 = 180,000

Or, N2 = 7200

CROSSOVER QUANTITY BETWEEN LOCATION B AND LOCATION D IS 4800 UNITS

CROSSOVER QUANTITY BETWEEN LOCATION B AND LOCATION C IS 7200 UNITS

For location D to be the most economical site for quantity N :

Or, 25.N < 120,000

Or, N < 4800

B ) 850,000 + 110.N < 1150,000 + 60.N ( i.e. total cost for location D < Total cost for location C )

Or, 50.N < 300,000

Or, N < 6,000

Taking into account both the constraints i.e. N < 4800 and N < 6000, we can say N < 4800

Therefore if the quantity is between 1 and 4799 units , location D is the most economical site

IF THE QUANTITY IS BETWEEN 1 AND 4799 UNITS, THEN THE LOCATION D IS THE MOST ECONOMICAL SITE

For location C having the lowest total cost :

25.N > 180,000

Or, N > 7200

   Or, 50.N > 300,000

Or, N > 6000

Taking into account both the constraints i.e. N > 7200 and N > 6000 , we can say N > 7200

HOWEVER, LOCATION C HAS THE LOWEST TOTAL COST FOR ANY QUANTITY ABIVE 7200 UNITS

CROSSOVER QUANTITY BETWEEN LOCATION B AND LOCATION D IS 4800 UNITS

CROSSOVER QUANTITY BETWEEN LOCATION B AND LOCATION C IS 7200 UNITS

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