Question $2$

a$.$ An operations manager has narrowed down the search for a new factory to three locations. The fixed and variable costs associated with each location are given in Table $3$ below.

i$.$ Write an equation for the total costs of each location.

ii$.$ Calculate the point where the costs lines intersect.

iii. Over which volume of output is each location preferred based on costs?$[3$ marks$]$

b$.$ Angella Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown in table $4$ below. Also, the volume from each source is provided.

i$.$ Calculate the coordinates for the centre of gravity location.

c$.$ A clothing chain is considering two different locations for a new retail outlet. They have identified the four factors listed in table $5$ as the basis for evaluation, and have assigned weights as shown. The manager has rated each location on each factor, on a $100-$point basis, as shown under the respective columns for Calliaqua and Layou in table $5$ below.

i$.$ Calculate the weighted score for Calliaqua and Layou.

ii$.$ Which location should be chosen and why?