(Solved): Consider a linear program in standard inequality form: maximise cTx subject to Ax b, (2) x ...

Consider a linear program in standard inequality form: maximise cTx subject to Ax ? b, (2) x ? 0 Let t> 0 be some constant and suppose we modify the program by multiplying the right-hand side of each constraint by t: maximise cx subject to Ax ? tb, x ? 0 (i) Show that x is a feasible solution of program (2) if and only if tx is a feasible solution of program (3). (ii) Show that if program (2) is unbounded then the program (3) is unbounded. (iii) Show that if tx is an optimal solution of program (3) then x is an optimal solution of program (2). Hint: it may be easier to prove the contrapositive: that if x is not an optimal solution for (2) then tx is not an optimal solution to (3).