QUESTION $2[15$ Marks$]$Study the caselet provided below and answer the following questions.The management of DGB Enterprises has narrowed down the site selection for a new manufacturing facility to threepotential locations A$,$ B and C$.$ The information provided below shows the annual fixed costs and variable costs per unitof the product at each of three locations.INFORMATIONLocation Fixed costs Variable costs per unitA R$3000000$ R$50$B R$4500000$ R$25$C R$6000000$ R$15$After an extensive market survey, the operations analyst of DGB Enterprises has estimated a R$75$ target selling price foreach unit of the product expected to be produced at the facility.Required:$2\mathrm{.}1.$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 curvesof 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 wouldyou recommend for the location of the new manufacturing facility? $(1$ marks$)$