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Question: Lacourse Inc.'s inspection costs are listed below: Units Produced Inspection Costs January...

Lacourse Inc.'s inspection costs are listed below:

Units Produced Inspection Costs
January 430 $ 6,130
February 380 $ 5,639
March 449 $ 6,345
April 464 $ 6,483
May 406 $ 5,889
June 381 $ 5,642
July 456 $ 6,410
August 407 $ 5,902

Management believes that inspection cost is a mixed cost that depends on units produced.

Using the least-squares regression method, the estimate of the fixed component of inspection cost per month is closest to:

Multiple Choice

$1,759

$1,801

$5,639

$5,813

Solutions

Expert Solution

Let ’X’ be No of units produced and

Let ‘Y’ be Inspection costs for that month.

Unit variable cost = V = [n(Sum of (X*Y)) – (Sum of X * Sum of Y)]/[n(sum of X2) – (sum of X)2 ]

Total Fixed cost = F = [(sum of Y) – V * (Sum of X)]/ n

Month X Y X2 XY
Jan 430 6130 184900 79507000
Feb 380 5639 144400 54872000
Mar 449 6345 201601 90518849
Apr 464 6483 215296 99897344
May 406 5889 164836 66923416
Jun 381 5642 145161 55306341
Jul 456 6410 207936 94818816
Aug 407 5902 165649 67419143
3373 48440 1429779 609262909

We have,

N = 8,

Sum of X = 3373

Sum of Y = 48440

Sum of X2 = 1429779

Sum of XY = 20501347

Calculating the average variable cost per unit=

[n(Sum of (X*Y)) – (Sum of X * Sum of Y)]/[n(sum of X2) – (sum of X)2 ]

= [(8*20501347) – (3373*48440)] / [(8*1429779) – (3373)2]

=622656/61103

=10.19

Calculating the approximate total Fixed cost:

F = [(sum of Y) – V * (Sum of X)]/ n

=[48440-(10.19*3373)]/8

=(48440-34370.87)/8

=14069.13/8

=1758.64 approximately equals to $1759


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