Answer: c. shut down because it would cost more to produce and sell output than it would to shut down and lose all fixed costs.
Explanation:
The profit maximizing, monopolistically competitive firm maximises profit at the point where marginal revenue equals marginal costs.
If this point is below Average variable costs then that means that the company is not making enough to cover its variable costs. Should this be the case then the company should shutdown operations because variable costs are only there when the company is producing. If they shutdown then they will no longer incur them which would be the cheaper option.
They would take losses on the fixed costs but these have already been incurred so it would be better to lose the fixed costs than continue to make losses on variable costs.