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 _____________________

In a two stage wire drawing operation, the fractional reduction (ratio of change in cross sectional area to initial cross sectional area ) in the first stage is $$0.4.$$ The fractional reduction in the second stage is $$0.3.$$ The overall fractional reduction is