A standard machine tool and an automatic machine tool are

A standard machine tool and an automatic machine tool are being compared for the production of a component.

For line balancing the number of work stations required for the activities M, E and T would respectively be

Given data

Total cost of z₁ component by using standard machine tool,

(T_C)₁ =		30	+	22 × z₁		× 200 = 100 +	2200	z₁
		60		60			30

Total cost of z₂ component by using Automatic Machine tool,

(T_C)₂ =		2 +	5	× z₂		× 800 = 1600 +	2000	z₂
			60				30

Let break even point be z number of components

∴ 100 +	2200	z = 1600 +	2000z
	30		30

or	200	z = 1500
	30

or z =	1500 × 30	= 225
	200

Alternately:
Let N be the Break even number
At Break even point

	1	+	22	.N		=		2 +	5N		×	800
	2		60						60			200

⇒	1	+	22	N =		2 +	5N		×	800
	2		60				60			200

⇒	1	+	22	N = 8 +	20N
	2		60		60

⇒	22	N −	20	N = −	1
	60		60		2

⇒		22 − 20		N =	16 − 1
		60			2

⇒ N =	15 × 60	= 225
	2 × 2