The Blacksburg Company is separating materials handling cost into fixed and variable components. The following data have been collected over a five-month period ( all amounts are in thousands): Direct Cost of Materials Month Labor Hours Materials Issued Handling Costs 1 4 $7 $1.60 2 5 5 1.70 3 6 4 1.80 4 7 8 1.90 5 8 6 2.00 Required:
(1) Determine the fixed and variable materials handling using direct labor hours as the measure of volume.
(2) Determine the fixed and variable materials handling cost by the method of least squares using direct labor hours as the measure of volume.

1. Variable cost = $0.10, fixed cost = $1.2

2. Variable cost = $0.10, fixed cost = $1.2

Explanation:

This question simply wants us to solve for variable cost and fixed cost using two different methods

1. Variable cost = (y2 - y1)/x1-x2

Y2 is the cost of at the highest level of activity = $2

Y1 is cost at lowest level of activity = $1.6

X2 = highest level of direct labor = 8

X1 = lowest level of labor = 4

V = variable cost = 2-1.6/8-4

= 0.4/4 = $0.1

Fixed cost = y2 - V*x2

= 2 - (0.1*8)

= $1.2

So the fixed cost here is $1.2 and variable cost is $0.10

2.

This requires us to solve using the least squares method. We first create a table as shown in the attachment and then solve for variable cost and fixed cost.

n = 5, xy = 55, x = 30, y = 9

We solve for a and b

b = 5x55-30x9/5x190-30²

= 275-270/950-900

= 5/50

= $0.10 this is the variable cost

a = 9-0.1(30)/5

= 6/5

= $1.2 this is the fixed cost

So using both methods in 1 and 2

Fixed cost = $1.2, variable cost = $0.10

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