[6] 4. Consider the linear program: maximize s+10t+r subject to 2s+5t+r<=16,
3s+t-3r<=12,4s+3t+3r<=20, and t,r>=0, but where s can be negative, zero,
or positive. Replace s by two variables, namely s=s_(1)-s_(2), where we impose the
condition s_(1),s_(2)>=0.
(a) The three constraints of this LP can be written as
[bigA][[s_(1)],[s_(2)],[t],[r],[w_(1)],[w_(2)],[w_(3)]]=[[16],[12],[20]]
where w_(1),w_(2),w_(3) are slack variables. Write out the matrix "big A.
(b) Can both s_(1) and s_(2) be basic in some dictionary of the simplex method? Justify
your answer using (part of) "big A."
[6]
4.
Consider the linear program: maximize s + 10t + r subject to 2s + 5t + r 16 3s+t-3r < 12, 4s+3t+3r < 20, and t,r> 0,but where s can be negative,zero or positive. Replace s by two variables, namely s = si - s2, where we impose the condition s1,s2 0.
(a) The three constraints of this LP can be written as
[s1 S2 t ["big A"] r W1 W2 W3
[16] 12 20
where w1,w2,w3 are slack variables. Write out the matrix "big A."
(b) Can both si and s2 be basic in some dictionary of the simplex method? Justify your answer using (part of)"big A."