There are eight different scenarios that correspond to the expectation (as of today) of the spot exchange rate E_$/€ on 26th August 2022: 1.4; 1.5; 1.6; 1.7; 1.8; 1.9; 2; and 2.1. Assume a trader can access the following instruments:

1. A European call option on the EUR, with a strike price of 1.75 Dollars per Euro and a premium of $0.05/€, and;
2. A European put option on the EUR, with a strike price of 1.75 Dollars per Euro and a premium of $0.04/€
   
Assume both of the above options expire on 26th August 2022. Assume both contracts are written on €100,000. Ignore the effects of interest rates and transaction costs.
a. In which scenario(s) will the trader profit by simultaneously buying both call and put options?                                     
b. For the strategy described in a), determine the full range of E_$/€  at which the trader will make a profit. What is the maximum loss that the trader can incur by pursuing the strategy described in a)?                             
c. In which scenario(s) will the trader profit by simultaneously selling both call and put options?                                               
d. For the strategy described in c), determine the full range of E_$/€  at which the trader will profit. What is the maximum profit that the trader can make by pursuing the strategy described in c)?    
e. Comment on when it is preferable to simultaneously buy both options. Similarly, explain when it is preferable to simultaneously sell both options.