Question

Problem: In a small car factory, a car type is manufactured by hand. The workers are paid with 1 USD per item manufactured. It is found that when a worker manufactures 80 items per day, 5% of them are rejected as scrap. If the worker produces 90 items/day, then 10% of them are rejected as scrap and if he produces 100 items/day 15% is rejected as scrap. The cost of materials used is 1,25 USD per item and the rejected items cannot be used again. There are some general expenses of 25 USD per day per per worker, independent of severe fluctuations in the production. Questions: (a) At which of these three production rates the workers receive the highest income? (b) At what production rate does the company have the lowest per unit cost?

Answer 1

Assumption used: it is assumed that worker is paid only for good units manufactured

Answer (a).

AT 100 units a day with 15% rejection worker earns highest income

as shown and calculated below

Wages at different level of production
If 80 Items are produced
	Income to Worker		=80*95%*1	=$76
If 90 Items are produced
	Income to Worker		=90*90%*1	=$81
If 90 Items are produced
	Income to Worker		=100*85%*1	=$85

Answer (b).

At 80 units with 5% scrap rate  production rate the company has the lowest per unit cost

as calculated and shown below

Units Introduce	80	90	100
Less: Scrape units	=80*5% =4	=90*10%=9	=100*15% = 15
Good Units produced	76	81	85

Cost of Production At Different level
		80 Units		90 Units		100 Units
Material Used	=125*80	10000	=125*90	11250	=125*100	12500
Labor cost		76		81		85
General Expenses per day		25		25		25
		10101		11356		12610
Good Units Produced		76 Units		81 Units		85 Units
Cost per unit	=10101/76	132.91	=11356/81	140.20	=12610/85	148.35

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