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

Question

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 three alternatives, A (new location), B (subcontract), and C (expand existing facilities). Alternative A would involve substantial fixed costs but relatively low variable costs: fixed costs would be $250,000 per year, and variable costs would be $500 per boat. Subcontracting would involve a cost per boat of $2,500, and expansion would require an annual fixed cost of $50,000 and a variable cost of $1,000 per boat.

1) What is the range of output that expansion would yield the lowest total cost?

A. 0-100

B. 34-400

C. 100-500

D. more than 400

2) Which alternative would yield the lowest total cost for an expected annual volume of 500 boats?

A. New location

B. Subcontract

C. Expansion

D. All of them are the same

Explanation / Answer

Given values:

Fixed costs = F and Variable costs = V

For Alternative A (New location): F = $250,000 per year, V = $500 per boat

For Alternative B (Subcontract): V = $2,500 per boat

For Alternative C (Expansion): F = $50,000 per year, V = $1,000 per boat

Solution:

Let the number of boats be represented by letter B, therefore, the given values can be written in mathematical equation as;

Total Cost for Alternative A = $250,000 + $500 B

Total Cost for Alternative B = $2,500 B

Total Cost for Alternative C = $50,000 + $1,000 B

(a) The number of boats at which alternative A and alternative B will incur same costs is calculated as;

$250,000 + $500 B = $2,500 B

2000 B = 250000

B = 125 boats

At 125 boats, alternative A and alternative B will incur same total costs.

(b) The number of boats at which alternative B and alternative C will incur same costs is calculated as;

$50,000 + $1,000 B = $2,500 B

1500 B = 50000

B = 33.33 or 34 boats

At 34 boats, alternative B and alternative C will incur same total costs.

(c) The number of boats at which alternative A and alternative C will incur same costs is calculated as;

$250,000 + $500 B = $50,000 + $1,000 B

500 B = 200000

B = 400 boats

At 400 boats, alternative A and alternative C will incur same total costs.

The range at which each alternative yields the lowest cost is:

A = 400 boats or more

B = 1 to 34 boats

C = 34 to 400 boats

1) The range of output that expansion (Alternative C) would yield the lowest total cost is Option (B) 34-400

2) Total cost for an expected annual volume of 500 boats:

Alternative A = $250,000 + $500 x 500 = $500,000

Alternative B = $2,500 x 500 = $1,250,000

Alternative C = $50,000 + $1,000 x 500 = $550,000

At 500 boats, Alternative A (New Location) yields the lowest cost.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.