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	12,800	2.2
L2	6,300	4.5
L3	8,100	3.1

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 4505 boats is location (Ex. type in as L1, L2, or L3)

Answer 1

Variable cost for L1 is the lowest and fixed cost is the highest so L1 would be suitable for large volumes

Variable cost for L2 is the highest and fixed cost is the lowest so L2 would be suitable for lower volumes

Location L3 would be suitable for medium volume.

Let's assume that for Volume <= Q1, Location L2 is the best

And for Volume >=Q2, Location L1 is the best

At Q1,

Total cost at L2 = Total Cost at L3

6300 + 4.5Q1 = 8100 + 3.1Q1

1.4Q1 = 1800

Q1 = 1285.71

At Q2,

Total cost at L1 = Total Cost at L3

12800 + 2.2.Q2 = 8100 + 3.1Q2

0.9Q2 = 4700

Q2 = 5222.22

a) Alternative 1:

For

Q > 5222 , Location alternative 1 would yield the lowest cost

b) Alternative 2

For

c) Q <=1285, Location alternative 2 would yield the lowest cost

Alternative 3

For 1285 < Q <= 5222, Location Alternative 3 would yield the lowest cost

d) L3

Q=4505, is in the range of alternative 3 so alternative 3 would yield the lowest cost