Ang company that produces pleasure boats has decided to expand one of its lines.
ID: 339319 • Letter: A
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)
Location
Fixed Cost/yr
variable cost/unit
L1
12,800
2.2
L2
6,300
4.5
L3
8,100
3.1
Explanation / Answer
Location 1 -
Total cost(location 1)= 12800+2.2Q
Total cost(location 2) = 6300+4.5Q
Total cost(location 3) = 8100+3.1Q
Point of indifference i.e. same costs can be found out by equating each of these to one another.
Location 1 = Location 2 => 12800+2.2Q = 6300+4.5Q => 2.3Q = 6500 => Q = 2826
Location 2 = Location 3 => 6300+4.5Q = 8100+3.1Q => Q = 1286
Location 3 = Location1 => 8100+3.1Q = 12800+2.2Q => Q = 5222
By substituting the values of the above in each of the total cost equations for locations,
a) Q>5222 ---> Location 1 is best
b) 0<Q<1286 ---> Location 2 is best
c) Q>1286 and Q<5222 ---> Location 3 is best
d) For an expected volume of 4505 boats, the alternative that would yield the lowest total cost is Location 3