$2\mathrm{.}1.$Formulate the cost functions for each of the three locations. $(3$ marks$)$

$2\mathrm{.}2.$Using a range of production output of $0200000$ units at intervals of $5000$ units, plot the total production cost curves

of the three locations on the same graph. $(5$ marks$)$

$2\mathrm{.}3.$Formulate the profit functions for each of the three locations. $(3$ marks$)$

$2\mathrm{.}4.$Determine the profits of the three locations for an estimated production and sales volume of $175000$ units per year.

$(3$ marks$)$

$2\mathrm{.}5.$Based on the estimated production and sales volume of $175000$ units per year, which of the three locations would

you recommend for the location of the new manufacturing facility?