A manufacturer has the following data regarding a product:
Fixed cost per month $$=$$ Rs. $$50,000$$
Variable cost per unit $$=$$ Rs. $$200$$
Selling price per unit $$=$$ Rs. $$300$$
Production capacity $$=$$ $$1500$$ units per month

If the production is carried out at $$80\% $$ of the rated capacity, then the monthly profit (in Rs.) is ______________

The uniaxial yield stress of a material is $$300$$ $$MPa.$$ According to Von mises criterion, the shear yield stress $$(in$$ $$MPa)$$ of the material is ___________.

A cube and a sphere made of cast iron (each of volume $$1000\,\,c{m^3}$$) were cast under identical conditions. The time taken for solidifying the cube was $$4$$ $$s.$$ The solidification time (in $$s$$) for the sphere is _____________________

The flowing stress (in $$MPa$$) of a material is given by $$\sigma = 500{\varepsilon ^{0.1}},$$
When $$\varepsilon $$ is true strain. The Young's modulus of elasticity of the material is $$200$$ $$GPa.$$ A block of thickness $$100$$ $$mm$$ made of this material is compressed to $$95$$ $$mm$$ thickness and then the load is removed. The final dimension of the block (in $$mm$$) is ____________