A project consists of $$7$$ activities. The network along with the time durations (in days) for various activities is shown in the figure.

The minimum time (in days) for completion of the project is _____________

Sales data of a product is given in the following table:

Regarding forecast for the month of June, which one of the following statements is TRUE?

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 ___________.