Misha has accepted a job in the mines and will produce one ore each day. At the market, he is able to buy or sell one ore for \$3, buy or sell bundles of three wheat for \$12 each, or $\textit{sell}$ one wheat for one ore. His ultimate goal is to build a city, which requires three ore and two wheat. How many dollars must Misha begin with in order to build a city after three days of working?
1. **Determine the resources needed to build a city:**
   - Misha needs 3 ore and 2 wheat to build a city.

2. **Calculate the ore Misha will have after three days:**
   - Misha produces 1 ore each day.
   - After 3 days, Misha will have \(3 \text{ ore}\).

3. **Determine the cost of obtaining wheat:**
   - Misha can buy bundles of 3 wheat for \$12.
   - Misha needs only 2 wheat, but he must buy 3 wheat as a bundle.

4. **Calculate the surplus wheat and its conversion:**
   - After buying 3 wheat, Misha will have 1 extra wheat.
   - Misha can sell 1 wheat for 1 ore.

5. **Calculate the total ore after selling the extra wheat:**
   - Initially, Misha has 3 ore from working.
   - Selling 1 wheat gives him 1 additional ore.
   - Total ore: \(3 + 1 = 4 \text{ ore}\).

6. **Determine the surplus ore and its conversion:**
   - Misha needs only 3 ore to build the city.
   - He has 1 extra ore.
   - Misha can sell 1 ore for \$3.

7. **Calculate the net cost:**
   - Misha needs \$12 to buy 3 wheat.
   - He can sell 1 extra ore for \$3.
   - Net cost: \( \$12 - \$3 = \$9 \).

Conclusion:
Misha must begin with a minimum of \$9 to build a city after three days of working.

The final answer is \( \$ \boxed{9} \).