Thermoplastic polymers are used often in 3-D printing. Polylactic acid (PLA) is a commonly used material. In general, temperatures within a range of can be programmed into the machines and successful fabrication of printed items depends upon precisely controlling the viscosity within the extrusion head and on the part itself. The viscosity of PLA depends on temperature and molecular weight according to [42]:

\[\eta(P a \cdot s)=89400\left(\frac{M_{w}}{1 \times 10^{5}}\right)^{3.38} \exp \left[\frac{190(\mathrm{~kJ} / \mathrm{mol})}{R}\left(\frac{1}{T}-\frac{1}{373(K)}\right)\right]\]

For fabricating a decorative item, small droplets are required and so the viscosity must be in the range \(0.155-0.16\). What range of temperature and molecular weight will allow us to produce the part?