Randburg Ltd is a manufacturing company that is about to launch a new product: Product Y. Details of the variable costs

Question

Randburg Ltd is a manufacturing company that is about to launch a new product: Product Y. Details of the variable costs incurred in producing one unit of Product Y are as follows: Labour R30 per hour Materials R40 per unit Variable overheads R10 per labour hour Additional Information Product Y is produced in batches of 25 units. The first batch of 25 units is expected to take 15 labour hours. There will be 80% learning curve that will continue until 60 batches have been produced. There after learning will stop, and the average time taken for the 60th batch will be same for the remaining batches. The total output expected is 100 batches. Required: a. Calculate the time required to produce the 60th batch of Product Y [15] b. Calculate the total variable cost of the 60th batch of Product Y [10] c. Calculate the total time take to manufacture 100 batches [5] Critically discuss the three conditions that must exist in the production process of Product Y, for the learning curve effect to be

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a) Time taken to produce first batch 15 Average time taken for 2 batches 12 Percent of first batch 80% (12/15) Average time taken for 4 batches 9.6 Percent of average time of 2 batches 80% (9.6/12) The time taken in this case follows 80% Learning Curvre The Equation will be Y=a(X^b) Y=Average time taken per batch a=Time taken to produce the first batch= 15 hours X=Cumulative bathces till learning curve is applicable= 60 b=Learning index For 80% Learning Curve b=Log0.8/Log2=-0.322 Y=Average time =15*(60^(-0.322))= 4.014 hours Total time required for 60 batches=60*4.014 240.81 hours If X=59 Y=Average Time for 59 batches=15*(59^(-0.322))= 4.04 Hours Total Time required to produce 59 batches=59*4.04 238.08 Hours a TIME REQUIRED TO PRODUCE 60TH BATCH=240.81-238.08 2.73 Hours b Total Variable Cost of the 60th batch: Direct Materials=40*25 1,000.00 RM Direct Labor=30*2.73 81.86 RM Variable Overhead=10*2.73= 27.30 RM TOTAL VARIABLE COST OF 60TH BATCH 1,109.16 RM c TIME TAKEN TO MANUFACTURE 100 BATCHES Time taken for first 60 batches 240.81 Hours Time taken for remaining (100-60=) 40 batches=40*2.73 109.20 Hours TIME TAKEN TO MANUFACTURE 100 BATCHES=240.81+109.20 350.01 Hours d THREE CONDITIONS THAT MUST EXIST: 1. Pressure or motivation to improve 2.Continuity of production 3.Constant improvement in production process

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Randburg Ltd is a manufacturing company that is about to launch a new product: Product Y

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Archived Solution

a)
		Time taken to produce first batch	15
		Average time taken for 2 batches	12		Percent of first batch	80%	(12/15)
		Average time taken for 4 batches	9.6		Percent of average time of 2 batches	80%	(9.6/12)

		The time taken in this case follows 80% Learning Curvre
		The Equation will be
		Y=a(X^b)
		Y=Average time taken per batch
		a=Time taken to produce the first batch=	15	hours
		X=Cumulative bathces till learning curve is applicable=	60
		b=Learning index
		For 80% Learning Curve
		b=Log0.8/Log2=-0.322
		Y=Average time =15*(60^(-0.322))=	4.014	hours
		Total time required for 60 batches=60*4.014	240.81	hours

		If X=59
		Y=Average Time for 59 batches=15*(59^(-0.322))=	4.04	Hours
		Total Time required to produce 59 batches=59*4.04	238.08	Hours
	a	TIME REQUIRED TO PRODUCE 60TH BATCH=240.81-238.08	2.73	Hours
	b	Total Variable Cost of the 60th batch:
		Direct Materials=40*25	1,000.00	RM
		Direct Labor=30*2.73	81.86	RM
		Variable Overhead=10*2.73=	27.30	RM
		TOTAL VARIABLE COST OF 60TH BATCH	1,109.16	RM

	c	TIME TAKEN TO MANUFACTURE 100 BATCHES
		Time taken for first 60 batches	240.81	Hours
		Time taken for remaining (100-60=) 40 batches=40*2.73	109.20	Hours
		TIME TAKEN TO MANUFACTURE 100 BATCHES=240.81+109.20	350.01	Hours

	d	THREE CONDITIONS THAT MUST EXIST:
		1. Pressure or motivation to improve
		2.Continuity of production
		3.Constant improvement in production process