If the futures price is lower than the spot price plus carrying cost, is there an arbitrage opportunity? If so, design a trading strategy.

Yes, there is an opportunity.

Explanation:

The non arbitrage parity means that the price of a future is the cost of the underlying asset plus its carrying costs, Y = X * (1 + Risk free). In this cases, future prices (Y) are cheaper than carrying the asset (X), so, in order to arbitrage, you have to go long with the future (buy it, but there isn't an exit of cash here), go short with the asset (sell it for y dollars), and buy the Risk free (with the money obtained in selling the asset). When the future expires, you will buy the asset at a price Y and (lower than X) and win the difference, with no risk.