= Solution
Let $h$ be the <stock> holding and let $c$ be the initial cost, so the cash holding is $b=c-10h$. Terminal <portfolio> wealth at <stock> price $s$ is $c+h(s-10)$. Dominating the <European call option> payoff at the three possible prices gives
$$
c-h\geq0,\qquad c\geq0,\qquad c+h\geq1.
$$
Adding the two endpoint inequalities yields $2c\geq1$. Equality is attained by $h=1/2$ and $c=1/2$, which imply $b=-9/2$. The corresponding terminal wealth is $0,1/2,1$ at $s=9,10,11$, respectively, compared with the required payoff $0,0,1$. \b[The cheapest super-replication strategy is]
$$
\boxed{\text{hold }\frac12\text{ share and }-\frac92\text{ units of cash};\qquad c_{\min}=\frac12.}
$$
The middle-state excess shows why this is <superhedging> rather than exact <claim replication>. The endpoint bound proves global minimality, without relying on the physical state <probabilities>.
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