Maximize $$\,\,\,\,Z = 15{x_1} + 20{x_2}$$
Subject to
$$\eqalign{ & 12{x_1} + 4{x_2} \ge 36 \cr & 12{x_1} - 6{x_2} \le 24 \cr & \,\,\,\,\,\,\,\,\,{x_1},\,\,{x_2} \ge 0 \cr} $$

The above linear programming problem has

The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ and $${\sigma _3} = 0\,\,MPa.$$ The yield strength of the material is $$200$$ $$MPa.$$ The factor of safety calculated using Tresca (maximum shear stress) theory is $${n_T}$$ and the factor of safety calculated using Von Mises (maximum distortional energy) theory is $${n_V}$$. Which one of the following relations is TRUE?

The part of a gating system which regulates the rate of pouring of molten metal is

Heat is removed from a molten metal of mass $$2$$ $$kg$$ at a constant rate of $$10$$ $$kW$$ till it is completely solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in $$kJ/kg$$) is ______________