A nylon solid rod of diameter $5\mathrm{.}0$ mm is manufactured using a single screw extruder. Calculate the production rate $(\frac{m}{m}in)$ if the operating extruder has a $7\mathrm{.}50$ cm diameter screw with a $2\mathrm{.}25$ m length, $17\mathrm{.}7$ flight angle, and a metering channel depth of $3\mathrm{.}50$ mm $.$ The screw is rotating at $45$ rpm $.$ The die land$-$length and diameter are $30\mathrm{.}0$ mm and $5\mathrm{.}0$ mm $,$ respectively. The polymer viscosity at the operating conditions is $185N\frac{s}{m^2},$ the melt density is $0\mathrm{.}820\frac{g}{c}{m}^3,$ and the solid density is $1\mathrm{.}12\frac{g}{c}{m}^3.($Hint: ignore the leak flow and the die swell$)$