Step 1: From previous calculations:
Happy first-time male = 10, Happy returning male = 10, Unhappy female = 40, Neutral male = 40, Neutral female = 60, Happy female = 60.
Step 2: Condition iii: Among first-time shoppers, ratio happy male : neutral male : unhappy female : remaining female = 1:1:1:2.
Let these be $b, b, b, 2b$. From earlier, happy first-time male = $b = 10$.
So neutral first-time male = 10, unhappy first-time female = 10, remaining first-time female = 20.
Step 3: Also, happy first-time female = unhappy first-time male (given). Let unhappy first-time male = $c$. Then happy first-time female = $c$.
Step 4: First-time female total = happy first-time female + neutral first-time female + unhappy first-time female = $c + \text{(neutral first-time femal(e)} + 10$.
From remaining first-time female = 20, that is neutral first-time female + unhappy first-time female? Actually "remaining female" means the other female categories besides happy, neutral, unhappy? Need to clarify.
Step 5: The numbers we need to compare:
- Neutral first-time female: unknown
- Unhappy first-time male: $c$
- Neutral first-time male: 10
- Unhappy first-time female: 10
- Happy returning male: 10
Step 6: The smallest among these is likely 10, and there are multiple with
10. But the question asks for "the lowest" and among the optionss, neutral first-time male is 10, which is one of the lowest.
Step 7: Final Answer: Number of neutral first-time male shoppers.