A post$-$tensioned prestressed concrete rectangular beam $300$ mm by $600$ mm in dimension is to be designed for a span of $7$ m$,$ to support a uniformly distributed of $1$ kN$/$m due to floor finish, together with an imposed load of $3$ kN$/$m$.$ If M$40$ concrete is used for the beam, construct the feasibility domain and determine the minimum prestress at mid$-$span. The minimum cover to reinforcement is $75$ mm$.$ Use allowable stresses as per IS $1343$:$2012.$ Assume the beam to be classified as Type$-$I for determination of allowable stresses in tension, and Zone$-$I for determination of allowable stresses in compression.