Find the value of the following portfolios of options at expiry, as a function of the share price:

(a) Long one share, long one put with exercise price E,

(b) Long one call and one put, both with exercise price E,

(c) Long one call, exercise price E₁, short one call, exercise price E₂, where E₁ < E₂,

(d) Long one call, exercise price E₁, long one put, exercise price E₂. There are three cases to consider,

(e) Long two calls, one with exercise price E₁ and one with exercise price E₂, short two calls, both with exercise price E, where E₁ < E < E₂.