Question

QUESTION 6

1. Ang company that produces pleasure boats has decided to expand one of its lines. The company is considering three Location alternatives. The cost structure for each location is given as shown in the table.
   

   Location	Fixed Cost/yr	variable cost/unit
   L1	13,515	2.3
   L2	8,605	3.1
   L3	6,388	4.1

   
   a) The range of output for location alternative 1 that would yield the lowest total cost is (Ex. In whole number, use Q, <, <=, >, >= to specify the range)
   
   b) The range of output for location alternative 2 that would yield the lowest total cost is (Ex. In whole number, use Q, <, <=, >, >= to specify the range)
   
   c) The range of output for location alternative 3 that would yield the lowest total cost is (Ex. In whole number, use Q, <, <=, >, >= to specify the range)
   
   d) The alternative would yield the lowest total cost for an expected annual volume of 1505 boats is location (Ex. type in as L1, L2, or L3)

Answer 1

Solution:

Let,

FC = Fixed Cost

VC = Variable Cost Per Unit

FC VC Locations L1 2.3 13515 8605 L2 3.1 4.1 L3 6388

Then,

Cross Over Point Between Two Locations = Absolute Difference Between Fixed Costs of Two Locations / Absolute Difference Between The Variable Cost Per Unit of Two Locations

Thus,

Coross Over Point Between L1 and L2 = 13515 Coross Over Point Between L2 and L3 = | 8605 Coross Over Point Between L1 and L3 13515 8605 1/1 2.3 - 6388 1/1 3.1 6388 1/1 2.3 3.1 | = 6138 4.1 | = 2217 4.1 | = 3959

(Rounded to the nearest whole number)

Hence,

Answer a:

The range of output for L1 resulting in the lowest total cost = 6138 and More

Answer b:

The range of output for L2 resulting in the lowest total cost = 2217 to 6138

Answer c:

The range of output for L3 resulting in the lowest total cost = 0 to 2217

Answer d:

TC = Total Cost = FC + (Q x VC)

Where, Q = 1505 Boats

Thus,

Total Cost For Location L1 = 13515 + (1505 x 2.3 ) = 16976.50 Total Cost For Location L2 = 8605 + (1505 x 3.1 ) = 13270.50 Total Cost For Location L3 = 6388 + (1505 x 4.1 ) = 12558.50

Hence, the alternative location L3 yields the lowest total cost for the expected annual volume of 1505 boats

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