Dawn's kenneling expansion: If she uses the added 1,000 square feet to accommodate larger dogs, the expected annual revenue is $22,000 in a strong economy and $16,000 in a weak economy. If instead she allocates the expansion to dogs under 30 pounds, the revenues are $20,000 (strong) and $17,500 (weak). Which option provides the best expected payout?

• A. Use expansion for dogs under 30 pounds, EV $19,000
• B. Use expansion for dogs under 30 pounds, EV $20,000
• C. Use expansion for large dogs, EV $19,600
• D. Use expansion for large dogs, EV $22,000

Answer: (C)

When evaluating which expansion yields the best payout, focus on the expected value of each option. Expected value is the average outcome you would get if the situation could occur many times, weighting each possible result by how likely it is.

Here there are two economy states: strong and weak. The large-dogs expansion yields 22,000 in a strong economy and 16,000 in a weak one. The small-dogs expansion yields 20,000 in a strong economy and 17,500 in a weak one. To compare, multiply each outcome by its probability and add them.

Using a 60% chance of a strong economy (and 40% weak) gives:

• Large-dogs: 0.6×22,000 + 0.4×16,000 = 13,200 + 6,400 = 19,600.

• Small-dogs: 0.6×20,000 + 0.4×17,500 = 12,000 + 7,000 = 19,000.

Thus expanding for large dogs produces the higher expected value: 19,600 versus 19,000. That’s why it’s the best option. If the probabilities were different, the result could change, but with these weights the larger-dog expansion is preferred.