The fixed and variable costs for three potential manufacturing plant sites for a
ID: 344419 • Letter: T
Question
The fixed and variable costs for three potential manufacturing plant sites for a rattan chair weaver areshown:
Site
Fixed Cost Per Year
Variable Cost per Unit
1
$ 600
$12.00
2
$1,000
$7.00
3
$2,200
$3.00
a) After rounding to the nearest whole number, site 1 is best below 80 units.
After rounding to the nearest whole number, site 2 is best between ____ and ______ units.
After rounding to the nearest whole number, site 3 is best above _____ units.
b) If the demand is 240 units, then the best location for the potential manufacturing plant is site 1, 2 or 3.
Site
Fixed Cost Per Year
Variable Cost per Unit
1
$ 600
$12.00
2
$1,000
$7.00
3
$2,200
$3.00
Explanation / Answer
To understand this question, lets first understand the meaning of Fixed cost per year & Variable cost per unit.
Fixed Cost Per year: It is the fixed expense of any manufacturing plant irrespective of the number of units produced. It includes expense like maintenance charges, building rent, administrative cost, audit cost etc.
Variable cost per unit: It the cost incurred to produce one unit of the goods. It includes expenses like raw material, logistics cost, labour cost etc.
In this case, if we want to calculate the total manufacturing cost of a unit over a year then we need to consider variable cost of total units produced & fixed cost of the manufacturing plant:
Total Manufacturing cost per year = Fixed cost per year + (Variable cost per unit)x(Number of units produced)
a) After rounding to the nearest whole number, site 1 is best below 80 units.
After rounding to the nearest whole number, site 2 is best between ____ and ______ units.
After rounding to the nearest whole number, site 3 is best above _____ units.
Lets check if we produce one unit at each of these manufacturing unit:
Site 1: Manufacturing cost: 600 +12*1 = 612
Site 2: Manufacturing cost: 1000 + 7*1 = 1007
Site 3: Manufacturing cost:: 2200 + 3*1 = 2203
Thus, we can see site one is best in this case, now we need to check till what no. site one is best.
This can be done by randomly checking number of units produced in each units, as its already given site one is best till 80 units, so lets check the same:
Thus, as per case -1, site 1 is best till 80 units.
As per case IX, site 3 is best above 300 units.
Thus, site 2 is best between 80 to 300 units.
This answers part a.
b) If the demand is 240 units, then the best location for the potential manufacturing plant is site 1, 2 or 3.
We can check in case V, if 240 units are produced, production costs are as follows:
Site1 : $3,480
Site: $ 2,680
Site: $ 2,920
Thus, site 2 is best if 240 units are requried to produced.
Alternate Method:
Same can be solved by unitary method.
Let "x" units are produced then cost at Site 1 will be equal to site 2.
Then,
600 + 12*x = 1000 + 7*x
thus, x = 80
So, Site 1 is best till 80 units.
Let "y" units are produced then cost at Site 2 will be equal to site 3.
1000 + 7*y = 2200 + 3*y
thus, y = 300
Thus, Site 2 is best if units are produced between 80 to 300
& Site 3 is best is above 300 units are produced.
Case - I Case - II Case - III Case - IV Case - V Case - VI Case - VII Case - VIII Case - IX Case - X Site Fixed Cost Per Year Variable Cost per Unit No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced No. of units produced 80 90 120 200 240 250 275 290 300 310 1 $600 $12 $1,560 $1,680 $2,040 $3,000 $3,480 $3,600 $3,900 $4,080 $4,200 $4,320 2 $1,000 $7 $1,560 $1,630 $1,840 $2,400 $2,680 $2,750 $2,925 $3,030 $3,100 $3,170 3 $2,200 $3 $2,440 $2,470 $2,560 $2,800 $2,920 $2,950 $3,025 $3,070 $3,100 $3,130 Total production cost at each Site with different number of units