$3.$ Company A and Company B have been quoted the following rates:

Company A fixed $3\mathrm{.}65\%$ or floating LIBOR $+50$ basis points

Company B fixed $4\mathrm{.}00\%$ or floating LIBOR $+75$ basis points

a$.$ Design a swap that will produce a net gain of $5$ basis points per annum for each of the two companies.

b$.$ Design a swap that will produce a net gain of $6$ basis points per annum for Company A and a net gain of $4$ basis points per annum for Company B$.$

c$.$ Design a swap that will produce a net gain of $2$ basis points per annum for each of the two companies and $1$ basis point for an intermediary.