RR manufactures radar systems. It has just completed the manufacture of its firs
ID: 467742 • Letter: R
Question
RR manufactures radar systems. It has just completed the manufacture of its first newly designed system, RS-32. Manufacturing data for the RS-32 follow:
Direct material cost
$ 88000
per unit of RS-32
Direct manufacturing labor time for first unit
3800
direct manufacturing labor-hours
Learning curve for manufacturing labor time per radar system
85% cumaulative average
Direct manufacturing labor cost
$23
per direct manufacturing labor-hour
Variable manufacturing overhead cost
$12
per direct manufacturing labor-hour
Using the formula for an 85% learning curve, b = IN 0.85/IN 2 = -0.162519/0.693147= -0.234465
Requirement
Calculate the total variable costs of producing 2, 4, and 8 units.
Direct material cost
$ 88000
per unit of RS-32
Direct manufacturing labor time for first unit
3800
direct manufacturing labor-hours
Learning curve for manufacturing labor time per radar system
85% cumaulative average
Direct manufacturing labor cost
$23
per direct manufacturing labor-hour
Variable manufacturing overhead cost
$12
per direct manufacturing labor-hour
Explanation / Answer
In this case, Learning curve is used to calculate manufacturing time for producing units
tn= t1*n^(lnr/ln2)
ln0.85/ln2 = -0.234465
Manufacturing time for producing 2nd unit
t2 = 3800* 2^(-0.234465)
= 3,230 hours
Total variable cost of producing 2 units
Material cost =88000*2 =$176000
Labor cost=3800*23 + 3230*23 =$161690
Overhead cost =3800*12 + 3230*12 =$84360
Total variable cost = 176000 + 161690 + 84360
= $422,050
In similar fashion , we can calculate total variable costs of producing 4 and 8 units
For 4 units
Material cost =88000*4 =$352000
Labor cost=(3800 + 3230 + 2937 + 2746)*23 =$292,399
Overhead cost =(3800 + 3230 + 2937 + 2746)*12 =$152556
Total variable cost = 352000 + 292399 + 152556 =$796,955
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