(a)The profit is the revenue minus cost so we write:

\(\displaystyle{P}{\left({x}\right)}={R}{\left({x}\right)}−{C}{\left({x}\right)}\)

\(\displaystyle{P}{\left({x}\right)}={25}{x}−{\left({4.3}{x}+{75}\right)}\)

\(\displaystyle{P}{\left({x}\right)}={25}{x}−{4.3}{x}−{75}\)

\(\displaystyle{P}{\left({x}\right)}={20.7}{x}−{75}\)

(b)Using the profit function from (a), substitute x=50 for 50 caps:

\(\displaystyle{P}{\left({50}\right)}={20.7}{\left({50}\right)}−{75}\)

\(\displaystyle{P}{\left({50}\right)}={1035}−{75}\)

\(\displaystyle{P}{\left({50}\right)}={960}\rightarrow\${960}\)

\(\displaystyle{P}{\left({x}\right)}={R}{\left({x}\right)}−{C}{\left({x}\right)}\)

\(\displaystyle{P}{\left({x}\right)}={25}{x}−{\left({4.3}{x}+{75}\right)}\)

\(\displaystyle{P}{\left({x}\right)}={25}{x}−{4.3}{x}−{75}\)

\(\displaystyle{P}{\left({x}\right)}={20.7}{x}−{75}\)

(b)Using the profit function from (a), substitute x=50 for 50 caps:

\(\displaystyle{P}{\left({50}\right)}={20.7}{\left({50}\right)}−{75}\)

\(\displaystyle{P}{\left({50}\right)}={1035}−{75}\)

\(\displaystyle{P}{\left({50}\right)}={960}\rightarrow\${960}\)