Lauren Wang invented a simple stock index which has futures contracts traded on it. The index is composed of three stocks whose current values are $50, $120 and $80, respectively. The index is calculated as the sum of the three stock prices multiplied by 150. The first stock makes a dividend payment of $1.2 on every June 1 and Dec 1; the second stock makes a dividend payment of $2.2 on every Jan 1 and July 1; the third stock makes a dividend payment of $1.8 on every March 1 and Sept 1. Now is Oct 1, 2020, and the annual risk-free rate is 3% (continuous compounding).

a) What must be the October-2021-futures price on the index to avoid arbitrage (maturity is October 31, 2021)?

b) Is there an arbitrage opportunity if the October-2021-futures price is $38,225.45? If yes, show the transactions on one futures contract.