Answer:
(a) Alternative A = 401 or more
Alternative B = 0 to 33
Alternative C = 34 to 399
(b) Alternative C will yield the lowest total cost
Explanation:
Alternative A:
Fixed costs = FCa = $250,000
Variable costs per boat = VCa = $500
Alternative B:
Variable costs per boat = VCb = $2500
Alternative C:
Fixed costs = FCc = $50,000
Variable costs per boat = VCc = $1000
We have to find crossover point with the alternative which have nearest variable cost
Hence, we find crossover point between pair of Alternative A and C and pair of Alternative B & C
For A & C
Let the crossover point be x
FCa + VCa * x = FCc + VCc * x
250,000 + 500x = 50000 + 1000x
x = 400
Higher number is preferred for Alternative with higher fixed cost.
Hence, for alternative A, the range should be 400 or more
For alternative C, the range should be less than 400
For B & C
Let the crossover point be y
FCb + VCb * y = FCc + VCc * y
0 + 2500x = 50000 + 1000y
y = 33.33
Higher number is preferred for Alternative with higher fixed cost.
Hence, for alternative C, the range should be 34 or more
For alternative B, the range should be less than 33
As seen from above,
Alternative A = 401 or more
Alternative B = 0 to 33
Alternative C = 34 to 399
Indifference points of 33.33 and 400 are not included in the above answer.
b.
For an annual volume of 150 boats, this fall in the range of 34 to 399
Hence, Alternative C will yield the lowest total cost for an expected annual volume of 150 boats
