A company that produces pleasure boats has decided to expand one of its lines. C
ID: 345085 • Letter: A
Question
A company that produces pleasure boats has decided to expand one of its lines. Current facilities are unsufficient to handle the increased workload, so the company is considering these 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 a fixed cost of $50,000, and expansion would require an annual fixed cost of $50,000 and a variable cost of $1,000 per boat.
a. Find the range of output for each alternative that would yield the lowest total cost. Round to the nearest whole number.
Explanation / Answer
Let the quantity involved = N
Therefore ,
Total cost of alternative A for n units in a year = $250,000 + $500.N
Total cost for alternative B for n units in a year = $50,000 + $2500.N
Total cost for alternative C for n units in a year = $50,000 + $1,000.N
For alternative A to be the lowest cost option:
Total cost of alternative A < Total cost for alternative B
Or, 250,000 + 500.N < 50,000 + 2500.N
Or, 2000.N > 200,000
Or, N > 100
Total cost for alternative A < Total cost for alternative C
Or, 250,000 + 500.N < 50,000 + 1000.N
Or, 500.N > 200,000
Or, N > 400
Taking into account both constraints i.e. N > 100 and N > 400, we can conclude that N > 400
For alternative B to be the lowest cost option :
Total cost for alternative B < Total cost for alternative A
50,000 + 2500.N < 250,000 + 500.N
Or, 2000.N < 200,000
Or, N < 100
Total cost for alternative B < Total cost for alternative C
50,000 + 2500.N < 50,000 + 1000.N
Or, 1500.N < 0
Or, N < 0
Taking into account both constraints simultaneously . i.e. N < 100 and N < 0 , the answer would be N < 0
However it is not possible to have N < 0 . Hence there is no feasible solution
For alternative C to be the lowest cost option :
Total cost for alternative C < Total cost for alternative A
Or, 50000 + 1000.N < 250,000 + 500.N
Or, 500.N < 200,000
Or, N < 400
Total cost of alternative C < Total cost of alternative B
Or, 50000 + 1000.N < 50000 + 2500.N
Or, 1500.N > 0
Or, N > 0
Taking into account both constraints i.e. N < 400 and N > 0 , we can conclude feasilble range to be 1 – 399 for alternative C to be the lowest cost option
AT OUTPUT > 400 , ALTERNATIVE 1 IS THE LOWEST COST OPTION
AT OUTPUT 1 – 399 , ALTERNATIVE C TO BE THE LOWEST COST OPTION
AT OUTPUT = 400, ALTERNATIVE A AND ALTERNATIVE C HAVE SAME COSTS
AT OUTPUT > 400 , ALTERNATIVE 1 IS THE LOWEST COST OPTION
AT OUTPUT 1 – 399 , ALTERNATIVE C TO BE THE LOWEST COST OPTION
AT OUTPUT = 400, ALTERNATIVE A AND ALTERNATIVE C HAVE SAME COSTS
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