In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain:
| Retailer I | Retailer II | Retailer III | Retailer IV | Capacity | |
|---|---|---|---|---|---|
| Supplier A | 11 | 16 | 19 | 13 | 300 |
| Supplier B | 5 | 10 | 7 | 8 | 300 |
| Supplier C | 12 | 14 | 17 | 11 | 300 |
| Supplier D | 8 | 15 | 11 | 9 | 300 |
| Demand | 300 | 300 | 300 | 300 |
The optimal cost of satisfying the total demand from all retailers is _____ rupees (answer in integer).
For a ball bearing, the fatigue life in millions of revolutions is given by $L = \left(\frac{C}{P}\right)^n$, where $P$ is the constant applied load and $C$ is the basic dynamic load rating. Which one of the following statements is TRUE?
Which one of the following failure theories is the most conservative design approach against fatigue failure?
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force $P = 100$ kN and a torque $T = 600$ N.m at the other end as shown. Assume that the axis of the cylinder is normal to the support.
Considering distortion energy theory with allowable yield stress as $300$ MPa, the factor of safety in the design is _____ (rounded off to 1 decimal place).
