Question

Due to increase in demand for​ Mazda's popular model​ XII, their production manager has narrowed the search for a new facility location to three​ sites: A,​ B, and C to locate a new production facility to build their​ new-model XII. The objective is to identify a site with minimum production​ cost, where cost is measured by the annual fixed cost plus variable cost per unit. Both the annual fixed costs and variable costs are provided​ below:

                                                                                                   

Location	Fixed Costs		Variable Costs per unit
Upper AA	$ 12 comma 000 comma 000$12,000,000		$ 2 comma 600$2,600
Upper BB	$ 20 comma 000 comma 000$20,000,000		$ 2 comma 000$2,000
Upper CC	$ 30 comma 000 comma 000$30,000,000		$ 1 comma 100$1,100

Production manager is determined to identify the best lcation possible..

​a) Volume of production above which location

Upper CC

is recommended​ =

nothing

units ​(round your response up to the next whole​ number).

​b) Volume of production below which location

Upper AA

is recommended​ =

nothing

units ​(round your response up to the next whole​ number).

​c) Over what range of volume is location

Upper BB

​optimal?

A.Location

Upper BB

is always optimal because its cost line is always below that of A and C for all volume levels.

B.Location

Upper BB

is optimal for volumes above

13 comma 33413,334

units.

C.Location

Upper BB

is never optimal because its cost line always exceeds that of A or C for all volume levels.

D.Location

Upper BB

is optimal for volumes from

12 comma 00012,000

to

13 comma 33413,334

units

Answer 1

The total cost equation is written as:

TC(Q) = F + V * Q

Where, F, V, and Q are the Fixed cost, Unit variable cost, and Volume respectively.

TC_A = 12,000,000 + 2,600 Q
TC_B = 20,000,000 + 2,000 Q
TC_C = 30,000,000 + 1,100 Q

Plot these three straight lines on a single 2-D plot to find the points of indifferences.

(a)

The volume of production above which location C is recommended​ = 12,000

(b)

The volume of production below which location A is recommended​ = 12,000

(c)

C. Location B is never optimal because its cost line always exceeds that of A or C for all volume levels