This problem is not as complex as it looks. In particular, you do not need to use the information given about the n and D0 values for the MTSH model; they're completely unnecessary for solving the problem. The primary difficulty is that Alpen does not do a very good job of describing either the OER or the "m" value.
Carefully reading what he's describing will tell you that in both cases--the OER definition and the definitions of the parameters in the m/k model--the crucial parameter is the ratio of the dose required for a given effect in the absence of oxygen to the dose required to produce the same effect in the presence of oxygen.
Thus if 90% cell killing (10% survival, or S/S0 = 0.1) is the chosen biological endpoint, then the OER will be the ratio of the dose required to kill 90% of the cells in the absence of O2 to the dose required to 90% of the cells in the presence of O2. In this case, for high [O2], the OER is 2.81, and in fact the OER flattens out to 2.81 at a relatively low [O2].
Thus based on the assertion that when [O2] >> K, the value of m will simply be the ratio of the dose required for a given effect without oxygen to the dose required with oxygen--i.e., m = OER itself for large [O2]. In a moment we'll calculate K and reconfirm that in fact the values of [O2] are high enough that we can ignore K.
Thus m = 2.81.
To calculate K, note that when [O2] = K,
OER = (m+1)/2 = 3.81 / 2 = 1.905.
From the curve when can see that OER = 1.905 at about
[O2] = 1%. Thus
K = 1%.
We can see that the OER rises to 2.81 values at [O2] values
substantially above that one and stays there.
Finally the ratio of type 1 repair to type 2 repair is expressed as
n1/n2 = m/2 = 1.405.