Answer:
42.85 m/min
Explanation:
To save cost, the tools should not be changed frequently if the tool cost or tool change time is high
[tex]The\ operator\ and\ machine\ tool\ rate =C_o=\$36/hr=\frac{\$36}{1\ hr*\frac{60\ min}{1\ hr} } =\$0.6/min[/tex]
The tooling cost per cutting edge = [tex]C_t[/tex] = $4.25
n = 0.13, C=75 (m/min), tool change time = [tex]t_t=4\ min[/tex]
Therefore the cutting speed for minimum cost is given as:
[tex]v_{max}=\frac{C}{[\frac{C_o}{(\frac{1}{n}-1 )(C_o*t_t+c_t)} ]^n} \\\\Substituting:\\\\v_{max}=75{[\frac{0.6}{(\frac{1}{0.13}-1 )(0.6*4+4.25)} ]^{0.13}} \\\\v_{max}=42.85\ m/min[/tex]
