A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs Rs. 150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is Rs. ____________ (rounded off to 1 decimal place).
$$ \begin{array}{|c|c|} \hline \text { Order quantity } & \text { Unit price(Rs.) } \\ \hline \text { 1 to 499 } & 9.0 \\ \hline \text { 500 to 999 } & 8.5 \\ \hline \text { 1000 or more } & 8.0 \\ \hline \end{array} $$A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________hours (answer in integer).
$$ \begin{array}{|c|c|c|} \hline \text { Activity } & \text { Immediate predecessor } & \text { Duration(hours) } \\ \hline A & - & 4 \\ \hline B & A & 8 \\ \hline C & A & 5 \\ \hline D & B & 2 \\ \hline E & B & 7 \\ \hline F & C & 6 \\ \hline G & D & 3 \\ \hline H & E, F, G & 9 \\ \hline \end{array} $$The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least $10^6$ loading cycles, as per the Soderberg law. Considering a factor of safety of 2 , the maximum applied tensile principal stress is