1. **Problem:** A firm's production was 4000 units in 2000 and planned to be 10000 units in 2010. Assuming linear increase, estimate production in 2004. 2. **Formula:** For linear growth, production $P$ at year $t$ is given by $$P = P_0 + r(t - t_0)$$ where $P_0$ is initial production, $t_0$ initial year, and $r$ is rate of increase per year. 3. **Calculate rate $r$:** $$r = \frac{P_{2010} - P_{2000}}{2010 - 2000} = \frac{10000 - 4000}{10} = 600$$ units per year. 4. **Estimate production in 2004:** $$P_{2004} = 4000 + 600 \times (2004 - 2000) = 4000 + 600 \times 4 = 4000 + 2400 = 6400$$ units. **Answer:** The estimated production in 2004 is **6400 units**.