Ang company that produces pleasure boats has decided to expand one of its lines.

Question

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

7,580

3.3

L2

5,358

4.4

L3

12,890

2.4

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 5505 boats is location  (Ex. type in as L1, L2, or L3)

Location

Fixed Cost/yr

variable cost/unit

L1

7,580

3.3

L2

5,358

4.4

L3

12,890

2.4

Explanation / Answer

L1 L2 L3 Fixed Cost (A) $7,580.00 $5,258.00 $12,890.00 Variable Cost per unit (B) $3.30 $4.40 $2.40 L2 will be cheapest at lower range of output, then L1 and finally L3. This is because L2 has lowest fixed cost followed by L1 and L3 Indifference Point between L1 and L2 Let the number units be x at indifference point X = Change in Fixed Cost / Change in Variable Cost X = 2322 / 1.1 X = 2110.91 units So Upto 2110 units, L2 is cheaper and from 2111 units L1 is cheaper Indifference Point between L1 and L3 Let the number units be x at indifference point X = Change in Fixed Cost / Change in Variable Cost X = 5310 / 0.90 X = 5900 So upto 5899 unit L1 is cheaper and from 5901 units L3 is cheaper and 5900 is the indifference point Effective Range Location Preference Q >= 0, < 2111 L2 Q >= 2111, = 5900 L3 Expected Cost at 5505 units Fixed Cost Variable Cost Units Cost a b c a + b*c L1 $7,580.00 $3.30 5505 $25,746.50 L2 $5,258.00 $4.40 5505 $29,480.00 L3 $12,890.00 $2.40 5505 $26,102.00 As stated above, L1 would be cheapest when the range of output is between 2111 - 5900 This is further substantiated from calculation where cost comes down to $25746 at L1 which is cheapest among all options.

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