A company that produces pleasure boats has decided to expand one of its lines. Current facilities are insufficient to handle the increased workload, so the company is considering there alternatives, N (new location), S (subcontract), E (expand existing facilities). Alternative N would involve substantial fixed costs but relatively low variable costs: fixed costs would be $250,000 per year (for the new facility), and variable costs would be $500 per boat. a. Find the range of output for each alternative that would yield the lowest total cost.

A or more

B to

C to

b. Which alternative would yield the lowest total cost for an expected annual volume of 150 boats?

A

B

C

(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

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