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 cost 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$ an a variable cost of $$1,000$ per boat.

a$.$ Find the range of output for each alternative that would yield the lowest total cost.

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

c$.$ What other factors might be considered in choosing between expansion and subcontracting?