Question

2. Machine components are manufactured in a factory at a rate of about 80 per day. The actual daily production is described by the following probability distribution: Production per Probability 0.03 0.07 0.14 0.17 0.14 0.12 0.10 0.08 0.07 0.05 0.03 75 76 78 79 80 81 82 83 84 85 At the end of each day's production, components are placed on a lorry and delivered overnight to customers. The lorry can take a maximum of 80 components, and will depart for delivery to customers even if it is holding less than 80 components at the end of the day. Any components in excess of 80 are carried over until the following day, and added to that day's production. (0) Simulate 20 days of this situation to estimate the mean number of components left waiting to be delivered after the lorry has departed each day, and the mean number of empty spaces in the lorry. Use the following set of random numbers: Day 1:0.875 Day 5:0.252 Day 9:0.895 Day 13:0.320 Day 14:0.841 Day 15:0.430 Day 16:0.144 Day 17:0.670 Day 18:0.229Day 19:0.933 Day 20:0.736 Day 2: 0.858 Day 6:0.501 Day 10:0.670 Day 3: 0.030 Day 7: 0.168 Day 11:0.902 Day 4: 0.654 Day 8:0.033 Day 12:0.300 (ii) If instead of the probability distribution given the daily production has a Normal Distribution with mean 79.5 and standard deviation 2.5, use the same random numbers as in part (i) to simulate 20 days of operation to estimate the same quantities as before.

Answer 1

Actual Variable overhead rate per hr = $170,000/(24000*2) = $3.54 per hr
Actual FOH rate per hr = $450,000/(24000*2) = $9.38 per hr

Factory overhead volume variance represents the difference between the budget allowance and the standard expenses charged to work in process (standard hours allowed × standard overhead rate)
Factory overhead volume variance (FOHVV) = Budgeted allowance based on standard hours allowed* – Overhead charged to production**

*Budgeted fixed expenses + variable expenses (standard hours allowed for actual production × variable overhead rate)

**Standard hours allowed × Standard overhead rate

SO FOHVV =(24000*2*$9.38+ 2*24000* $3.54) - ($450000+2*24000*$3.50)
ie VV = $2,160 = $2160 U....... >ans(a)

The controllable variance is the difference between actual expenses incurred and the budget allowance based on standard hours allowed for work performed. This variance may be favorable or unfavorable.
Controllable variance (CV) = Actual Factory Overhead (AFOH) - Budgeted Allowance Based on Standard Hours Allowed (BFOH)
ie CV = ($450000+$170,000) - ($450,000+ 25000*2*$3.50) = $(5,000) = $5000 F ..Ans(b)

Total factory overhead cost variance (TOHCV) is nothing but Over/Under absorbed OHs

ie TOHCV = Total OH Cost absorbed - Total OH Cost incurred
ie TOHCV = Actula o/p *Budgeted rate pu -Actual o/p*Actual rate pu
ie TOHPU = (24000*2*9.00 + 24000*2*$3.50) - (24000*2*$9.38+24000*2*$3.54) = $(20,160)
ie TOHPU = $20,160 U ....ans(c)