$4.$ Johnson Mining Company $($JMC$),$ primarily mines gold, and is currently trading at $$54\mathrm{.}55/$share$.$ The CEO of the company suddenly dies, and no one is sure what affect this will have on the company in the short term. Assume a $2\%$ annual interest rate. The following options are available. $(3$ points$)$

Spot Expiration Call Price Strike Price Put Price

$$54\mathrm{.}553$ Months $$12\mathrm{.}79$ $$50\mathrm{.}00$ $ $6\mathrm{.}28$

$$54\mathrm{.}553$ Months $$10\mathrm{.}49$ $$55\mathrm{.}00$ $ $8\mathrm{.}78$

$$54\mathrm{.}553$ Months $ $8\mathrm{.}57$ $$60\mathrm{.}00$ $$11\mathrm{.}66$

a$.$ Describe exactly how you would create a bottom straddle using the above options, and what your initial cost per share would be for this position.

b$.$ Draw a profit diagram of your position. Clearly indicate all breakeven points, and intercepts.

c$.$ Describe exactly how you would create a bottom strangle using the above options, and what your initial cost per share would be for this position

d$.$ Draw a profit diagram of your position. Clearly indicate all breakeven points, and intercepts.

e$.$ The price barely changes and JMC is now $$55\mathrm{.}42.$ What is your profit per share in each position above?

f$.$ What if instead the price moves to $$61\mathrm{.}00?$ What is your profit per share in each position above?