You hold a portfolio consisting of a $$5,000$ investment in each of $20$ different stocks. The portfolio beta is equal to $1\mathrm{.}21.$ You have decided to sell a coal mining stock $($b $=1\mathrm{.}00)$ at $$5,000$ net and use the proceeds to buy a like amount of a mineral rights company stock $($b $=2\mathrm{.}00).$ What is the new beta of the portfolio?

a$.$

$1\mathrm{.}2600$

b$.$

$1\mathrm{.}3573$

c$.$

$1\mathrm{.}1700$

d$.$

$1\mathrm{.}2900$

e$.$

$1\mathrm{.}1139$