A very large metal plate of thickness 𝑑 and thermal conductivity 𝑘 is cooled by a stream of air at temperature 𝑇∞ = 300 K with a heat transfer coefficient ℎ, as shown in the figure. The centerline temperature of the plate is TP. In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate? 

With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct? 

Which one of the options given represents the feasible region of the linear programming model:

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 45𝑋₁ + 60𝑋₂

𝑋₁ ≤ 45

𝑋₂ ≤ 50

10𝑋₁ + 10𝑋₂ ≥ 600

25𝑋₁ + 5𝑋₂ ≤ 750

A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the AM machine is a/10 mm and the nozzle follows a linear serpentine path parallel to the sides of the square layers with a feed rate of a/5 mm/min.

Ignore any tool path motions other than those involved in adding material, and any other delays between layers or the serpentine scan lines.

The time taken to fabricate this part is ___________ minutes.

(Answer in integer)