A solid sphere $$1$$ of radius $$'r'$$ is placed inside a hollow, closed hemispherical surface $$2$$ of radius $$'4r'.$$ The shape factor $${F_{2 - 1}}$$ is ...

The annual requirement of rivets at a ship manufacturing company is $$2000$$ $$kg.$$ The rivets are supplied in units of 1 kg costing Rs. $$25$$ each. If it costs Rs. $$100$$ to place an order and the annual cost of carrying one unit is $$9\% $$ of its purchase cost, the cycle length of the order (in days) will be _______________

In the notation $$(a/b/c) : (d/e/f)$$ for summarizing the characteristics of queuing situation, the letters $$‘b’$$ and $$‘d’$$ stand respectively for

For the linear programming problem:
$$\eqalign{ & Maximize\,\,\,\,\,Z = 3{x_1} + 2{x_2} \cr & Subject\,\,to\,\,\,\, - 2{x_1} + 3{x_2} \le 9 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1} - 5{x_2} \ge - 20 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$

The above problem has