Question at position 4 Dara specializes in Dolphin rescue from poaching off the Florida coast. The cost of transporting a dolphin is extremely expensive and Dara is trying to find ways to cut back on her cost she knows the equipment including the truck, crane and tank the dolphin is transported in cost $3.3 million annually. Additionally, the veterinary staff and truck drivers have a variable cost of $54,000 per dolphin. Dara found a new transportation company that can transport dolphins for $780,000 per dolphin. How many dolphins would Dara have to rescue each year to make the transportation company equal to Dara conducting it herself? (round your answer to the nearest whole number) Dara specializes in Dolphin rescue from poaching off the Florida coast. The cost of transporting a dolphin is extremely expensive and Dara is trying to find ways to cut back on her cost she knows the equipment including the truck, crane and tank the dolphin is transported in cost $3.3 million annually. Additionally, the veterinary staff and truck drivers have a variable cost of $54,000 per dolphin. Dara found a new transportation company that can transport dolphins for $780,000 per dolphin. How many dolphins would Dara have to rescue each year to make the transportation company equal to Dara conducting it herself? (round your answer to the nearest whole number) [input]

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BlackTom AI · Accepted Answer

First, restate the problem to ensure understanding: Dara currently incurs fixed annual costs to transport a dolphin herself, amounting to 3.3 million dollars, plus a variable cost of 54,000 dollars for each dolphin handled. A third-party transport company offers to transport each dolphin for 780,000 dollars. The question asks how many dolphins Dara would need to rescue per year for the third-party option to cost the same as doing it herself, rounding to the nearest whole number.

Next, translate the costs into a mathematical equation. If N dolphins are rescued per year, the total annual cost of Dara handling it herself is:
- Fixed costs: 3.3 million dollars
- Variable costs: 54,000 dollars per dolphin × N = 0.054 million × N
So total self-handling cost = 3.3 + 0.054N (in millions).

The total cost of using the transportation company for N dolphins is simply 0.78 million dollars per dolphin × N = 0.78N (in millions).

Set the two costs equal to find the break-even point:
3.3 + 0.054N = 0.78N

Now solve for N. Subtract 0.054N from both sides to collect N terms on the right:
3.3 = 0.78N − 0.054N = 0.726N

Divide both sides by 0.726 to isolate N:
N = 3.3 / 0.726 ≈ 4.545

Since you can’t rescue a fraction of a dolphin, round to the nearest whole number. 4.545 rounds to 5.

To sanity-check, evaluate costs at N = 5:
- Self-handling: 3.3 + 0.054×5 = 3.3 + 0.27 = 3.57 million
- Third-party: 0.78×5 = 3.9 million
These are not equal, but since 4.545 is the exact break-even, rounding up to 5 is the convention for a break-even decision where the third-party option becomes more economical at or above that point. If you plug N = 4, self-handling is 3.3 + 0.216 = 3.516 million, while third-party is 3.12 million, which shows the crossover occurs between 4 and 5, reinforcing that 5 is the nearest whole-number break-even or slightly favorable for outsourcing depending on rounding policy.

In summary, the calculation yields N ≈ 4.545, which rounds to 5 dolphins per year for the break-even comparison between Dara’s in-house transport and using the transportation company.

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