Confidence Intervals · Superchallenge problem

Two labs independently measure the same quantity. Lab A reports the 95% interval $(10,\ 14)$ and Lab B reports $(12,\ 14)$, both of the form estimate $\pm 1.96 \times$ standard error. The estimates are combined as $w\,\hat\theta_A + (1-w)\,\hat\theta_B$ with the weight $w$ that makes the variance as small as possible, and a 95% interval is built from the combination. Find its UPPER end. Round to the nearest hundredth.