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 in increased workload, so the company is considering three alternatives, A (new location), B (s ient to handle the Alternative A would involve substantial fixed costs but relatively low variable costs: fixed costs would be $310,000 per year, and variable costs would be $530 per boat. Subcontracting woul annual fixed cost of $58,000 and a variable cost of $1,080 per boat d involve a cost per boat of $2,580, and expansion would require an a. Find the range of output for each alternative that would yield the lowest total cost. (Leave no cells blank - be certain to enter "O wherever required. Round your answers to the nearest whole number.) b. Which alternative would yield the lowest total cost for an expected annual volume of 310 boats? OA

Explanation / Answer

We are given 3 alternatives here with the following costs:

Now, the total cost for each alternative, assuming we make x boats, is:

A: 310000 + 530x

B: 2580x

C: 58000 + 1080x

Let us find the points where the costs become equal between A & B, B & C and C &A (there are our critical points)

Equating A & B:

310000 + 530x = 2580x

x = 151.2 or 152 boats (If you plug in the values, you will note that for x<152, option B is cheaper. For x>153, option A is cheaper)

Let us equate B & C:

2580x = 58000 + 1080x

x = 38.66 or x = 39 boats

for x<39 boats, option B is cheaper. For x>39 boats, option C is cheaper

Let us equate C & A:

310000 + 530x = 58000 + 1080x

x = 458.18 boats

For x < 459 boats, C is cheaper. For x > 459 boats, A is cheaper

Combining all the three, the alternatives are

A: for > 458.18 (or 459) boats (458 if it is to be rounded to the closest number)

B: from 0 boats to 38.66 (or 39) boats

C: between 38.66 (or 39) and 458.18 (or 459) boats (458 if it is to be rounded to the closest number)

I am not sure if you want to round off to the next highest number or the closest number, hence I have included both the decimal and the integer answer (because ideally 151.2 boats should be rounded off to 152, but the closest whole number is 151). Since it is not clear in the question, I have included both the answers.

Qn b) If the output is 310 boats, clearly, the cheapest alternative will be Option C, expand existing facilities, as it falls in the bracket between 38.66 and 458.18 boats

Alternative Fixed Cost ($) Variable ($/boat) A 310000 530 B 0 2580 C 58000 1080

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