$(1)$ A manager has received an analysis of several cities being considered for a new order fulfillment center $($warehouse$)$ for the Shop at Home Network. The scores $($scale is $10$ points $=$ best$)$ are contained in the table below.

$($a$)$ If the manager weighs the factors equally, how would the locations be ranked?

$($b$)$ If transportation costs and real estate costs are given weights that are triple the weights of the others, should the locations be ranked differently?

$\backslash$table$[[,$Location$],[$Factor$,$W$,$X$,$Y$,$Z$,],[$Business services,$3,8,9,8,],[$Community services,$3,6,8,9,],[$Real estate cost,$9,6,8,8,],[$Construction costs,$8,9,5,9,],[$Operating costs,$9,7,9,9,],[$Transportation costs,$9,8,6,4,]]$

$(2)$ A manufacturing company preparing to build a new plant is considering three potential locations for it$.$ The fixed and variable costs for the three alternative locations are presented below.

$($a$)$ Complete a numeric locational cost$-$volume analysis.

$($b$)$ Indicate over what range each of the alternative's A$,$ B$,$ C is the low$-$cost choice.

$($c$)$ Draw the solution graphically

$($d$)$ Is any alternative never preferred? Explain.

$\backslash$table$[[$Cost$,$A$,$B$,$C$],[$Fixed $($$$),230,000,200,000,240,000],[$Variable $($$ per unit$),26,30,25]]$