If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that

A job shop incurs a cost of Rs.$$60$$/- per day for each day a job is in the shop. At the beginning of a month there are five jobs in the shop with the following data:

Which schedule will minimize the total cost?
What is the minimum total cost?
Which jobs (if any) fail to meet their due dates?

A solid shaft can resist a bending moment of $$3.0$$ $$kNm$$ and a twisting moment of $$4.0$$ $$kNm$$ together, then the maximum torque that can be applied is

If the ratio of the diameter of river hole to the pitch of rivets is $$0.25$$, then the tearing Efficiency of the joint is