A furniture manufacturer produces chairs and tables. The wood-working department is capable of producing $$200$$ chairs or $$100$$ tables or any proportionate combinations of these per week. The weekly demand for chairs and tables is limited to $$150$$ and $$80$$ units respectively. The profit from a chair is Rs.$$100$$ and that from a table is Rs.$$300.$$

$$(a)$$ Set up the problem as a Linear Program
$$(b)$$ Determine the optimum product mix for maximizing the profit.
$$(c)$$ What is the maximum profit?
$$(d)$$ If the profit of each table drops to Rs.200 per unit, what is the optimal mix and profit?

The supply at three sources is $$50, 40$$ and $$60$$ units respectively whilst the demand at the four destinations is $$20, 30, 10$$ and $$50$$ units. In solving this transportation problem

A static load is mounted at the center of a shaft rotating at uniform angular velocity. This shaft will be designed for

Large speed reductions (greater than $$20$$) in one stage of gear train are possible through