Consider a market with an incumbent firm and a new entrant E producing a homogenous product and competing in quantities. The incumbent has a technology with cost function C_I(q)=30q while the entrant produces with C_E(q)=20q.

The inverse demand is given by P(q)=180-q.

Suppose the entrant is credit-constrained and has to repay an amount of D=400 at the end of the period. If the entrant is not able to cover this amount with its profits, the firm has to leave the marketplace.

What is the minimum quantity q_Ithat makes sure the entrant is unable to repay the amount of D=400? [Please use the next smallest integer. That is instead of 50+epsilon, use 50.]