$6\mathrm{.}3-5.$ Consider the two versions of the dual problem for the radia$-$

tion therapy example that are given in Tables $6\mathrm{.}14$ and $6\mathrm{.}15.$ Review

in Sec. $6\mathrm{.}3$ the general discussion of why these two versions are

completely equivalent. Then fill in the details to verify this equiva$-$

lency by proceeding step by step to convert the version in Table $6\mathrm{.}14$

to equivalent forms until the version in Table $6\mathrm{.}15$ is obtained.

TABLE $6\mathrm{.}14$ One primal$-$dual form for the radiation therapy example

Primal Problem

TABLE $6\mathrm{.}15$ The other primal$-$dual form for the radiation therapy example

Primal Problem