Required informatio Problem 6-42 Continuation of Preceding Problem; Computing Le
ID: 2331847 • Letter: R
Question
Required informatio Problem 6-42 Continuation of Preceding Problem; Computing Least-Squares Regression Estimates; Comparing Multiple Methods (Appendix) (LO 6-1, 6-2, 6-5, 6-6, 6-8) [The following information applies to the questions displayed below.] Martha's Vineyard Marine Supply is a wholesaler for a large variety of boating and fishing equipment. The company's controller, Mathew Knight, has recently completed a cost study of the firm's material-handling department in which he used work measurement to quantify the department's activity. The control factor unit used in the work-measurement study was hundreds of pounds of equipment unloaded or loaded at the company's loading dock. Knight compiled the following data Units of Activity (hundreds of pounds Month JanuaryY February March April May une July August September October November December equipment loaded or unloaded) 2,700 2,500 2,200 1,900 3,100 3,300 2,900 2,700 3,500 2,000 2,100 2,300 Material- Handling Department Costs $12,600 12,200 11,700 11,100 12,000 13,900 12,900 12,300 13,200 11,500 12,250 12,250Explanation / Answer
Answers
n
x [units/hours]
y [cost]
X2
xy
Jan
2,700
$ 12,600.00
7,290,000
34,020,000
Feb
2,500
$ 12,200.00
6,250,000
30,500,000
Mar
2,200
$ 11,700.00
4,840,000
25,740,000
Apr
1,900
$ 11,100.00
3,610,000
21,090,000
May
3,100
$ 12,000.00
9,610,000
37,200,000
Jun
3,300
$ 13,900.00
10,890,000
45,870,000
Jul
2,900
$ 12,900.00
8,410,000
37,410,000
Aug
2,700
$ 12,300.00
7,290,000
33,210,000
Sep
3,500
$ 13,200.00
12,250,000
46,200,000
Oct
2,000
$ 11,500.00
4,000,000
23,000,000
Nov
2,100
$ 12,250.00
4,410,000
25,725,000
Dec
2,300
$ 12,250.00
5,290,000
28,175,000
12
31,200
$ 147,900.00
84,140,000
388,140,000
n
12
x
31,200
y
147,900
x2
84,140,000
xy
388,140,000
----Equations----
>Variable cost per unit = ‘b’
>Fixed Cost = ‘a’
Unit Variable Cost = b = [ (n xy) - (x. y) ] / [(nx2 ) – (x)2]
[ (n xy) - (x. y) ] = N [Numerator]
[(nx2 ) – (x)2] = D [Denominator]
Total Fixed Cost = a = [ (y) – (bx) ] / n
[ (y) – (bx) ] = N1 [Numerator]
---Solving for ‘b’: Calculation of Variable cost per unit---
N [Numerator]
=
(n
x
xy)
-
(x
x
y)
N [Numerator]
=
12
x
388140000
-
31200
x
147900
N [Numerator]
=
4657680000
-
4614480000
N [Numerator]
=
43200000
D [Denominator]
=
(n
x
x2)
-
(x)2
D [Denominator]
=
12
x
84140000
-
973440000
D [Denominator]
=
1009680000
-
973440000
D [Denominator]
=
36240000
b
=
N
/
D
b
=
43200000
/
36240000
b
=
1.19205298
----Solving for ‘a’: Calculation of Fixed Cost---
N1 [Numerator]
=
y
-
(b
x
x)
N1 [Numerator]
=
147900
-
1.19205298
x
31200
N1 [Numerator]
=
147900
-
37192.05298
N1 [Numerator]
=
110707.947
a
=
N1
/
n
a
=
110707.947
/
12
a
=
9225.662252
Fixed Cost Component
$ 9,226.00 [Value computed as ‘a’]
Variable cost component
$ 1.19 per unit [Value computed as ‘b’]
Total Monthly Cost = $ 9226 + $ 1.19 per unit of Activity
Total Monthly cost for 2700 units = $ 9226 + ($1.19 x 2700 units)
= 9226 + 3213
= $ 12,439
ANSWER: $ 12,439
n
x [units/hours]
y [cost]
X2
xy
Jan
2,700
$ 12,600.00
7,290,000
34,020,000
Feb
2,500
$ 12,200.00
6,250,000
30,500,000
Mar
2,200
$ 11,700.00
4,840,000
25,740,000
Apr
1,900
$ 11,100.00
3,610,000
21,090,000
May
3,100
$ 12,000.00
9,610,000
37,200,000
Jun
3,300
$ 13,900.00
10,890,000
45,870,000
Jul
2,900
$ 12,900.00
8,410,000
37,410,000
Aug
2,700
$ 12,300.00
7,290,000
33,210,000
Sep
3,500
$ 13,200.00
12,250,000
46,200,000
Oct
2,000
$ 11,500.00
4,000,000
23,000,000
Nov
2,100
$ 12,250.00
4,410,000
25,725,000
Dec
2,300
$ 12,250.00
5,290,000
28,175,000
12
31,200
$ 147,900.00
84,140,000
388,140,000
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