Suppose you have three positions in the following assets in euros: long on 10.000 calls (maturity T = 3 months, strike= 0.55, Delta (1 call) =0.533), short on 210000 calls (maturity T = 3 months, strike= 0.56, Delta (1 call) =0.468), short on 20000 puts (maturity T = 3 months, strike= 0.56, Delta (1 put) =-0.8944). You can make your portfolio delta-neutral (a) with a long position on 75062 euros (b) with a short position on 75062 euros; (c) with a long position on 75062 calls; (d) with a short position on 75062 puts.
I tried to compute the portfolio's Delta by summing the Delta of the derivatives an multiplying them for the number of options. Then I tried to dived the portfolio's delta by the derivatives' delta one by one to find out how many calls or puts i had to sell/buy to make the portfolio delta neutral. Then I tried to convert the results in euro but none of my attempets brough me somewhere near the number 75062. Can you please help me?