Please show all work.

Underlying at 1000 with rf=6%. You are looking at option chain with DTE of 28.

You are examining the following put back ratio spread positions:

Short 200 puts at strike of 950. IV for the put is 18% annually.

Long 300 puts at strike of 925. IV for the put is 21% annually.

a. Calculate delta for each leg as well as for the overall position

b. Calculate gamma for each leg as well as for the overall position

c. Calculate one day theta for each contract as well as for the overall position

d. Calculate vega value for each leg as well as for the overall position

e. Market dropped by $50 from $1000 to $950 in a single day, what is your PnL from delta, gamma, and theta respectively if IV did not change for the puts

f. What is the new position delta after question e's move? How do you use underlying to flatten the position delta?

g. Market dropped by $50 from 1000 to 950 in one day. If IV for 950 strike PUT IV goes up from 18% to 22%, and IV for 925 PUT goes up from 21% to 27%, what is your vega PnL as well as total PnL

h. What is the new position delta after the move in question g? How do you use underlying to flatten the position delta?