Consider a hemispherical furnace of diameter $ D = 6 \text{ m} $ with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300 K and 1200 K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is _______ kW (rounded off to the nearest integer).
Use Stefan-Boltzmann constant = $5.67 \times 10^{-8} \text{ W/(m}^2 \text{ K}^4 \text{)}$
A set of jobs $U, V, W, X, Y, Z$ arrive at time $t = 0$ to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.
| Job | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|
| Workstation 1 | 5 | 7 | 3 | 4 | 6 | 8 |
| Workstation 2 | 4 | 6 | 6 | 8 | 5 | 7 |
The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is
A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is