Complementing @BKay's answer, let's consider the labor market, which per assumptions is perfectly competitive. The equilibrium wage adjusts so that labor supply and labor demand equate and we have
$$L^s = L^d \implies 50w^* = L^d \implies w^* = L^d/50$$
Now the question is, how much will labor demand be? Given the specification of the production function and the fact that $K =100$, and assuming that we will either employ all $K$ or none at all, then we see that Labor Demand cannot exceed the value of $100$, because, if its was, say $101$, then we would have $Y = \min \{K,L\}=K$ and said Labor would not be used in production at all, so it is nonsensical to "demand" it. So we conclude that the maximum observable wage is $\max w = 2$. For the wage range $(0,2]$ labor supply will always be smaller than $100$, and so also labor demand and labor employed, and production will be carried using only labor and no capital, and the rest are @BKay's.
Note that this can be considered suboptimal, because if we employed all capital and no labor, we would have output equal to $100$, while we now have output of only $50$. Even if we assume that working does not generate disulity, higher output would be preferable since it expands the boundaries of the consumption set. So the central planner solution would be different than the market outcome.
Could an entity like a government use tax and subsidies to increase output? In other words assume that the model is
$$\max _{K,L^d}\pi = min [K, L^d] - r\cdot K - w\cdot L^d + s\cdot K$$
$$L^s = 50\cdot (1-\tau)w$$
$$L^s = L^d =L^*$$
and a balanced budget for the government
$$sK = \tau wL^*$$
Would we obtain something different?
