suppose you construct an butterfly position on Apple stocks as follows, with Apple stock currently trading at $400. all options have an expiration date of one year from today and the constant a>0.

1.Long one out-of-the-money put option with premium $5 and strike price of 400-a

2.Short one at-the-money put with premium $35

3.Short one at-the-money call with premium $45

4.Long one out-of-the-money call with premium $15 and strike price of $400+a

question:

a)draw the profit diagram at expiration for the Apple butterfly, with the constant a as a free parameter, assuming the risk-free interest rate is zero.

b)what is the minimum possible value for the profit at expiration for the Apple butterfly, expressed in terms of the parameter a? for what range of values for a does an arbitrage opportunity exist?