Question

A standard machine tool and an automatic machine tool are being compared for the production of a component. Following data refers to the two machines.

	Standard Machine tool	Automatic Machine tool
Setup time	30 min.	2 hours
Machining time per piece	22 min.	5 min
Machine rate	Rs. 200 per hour	Rs. 800 per hour

The breakeven production batch size above which the automatic machine tool will be economical to use, will be

• A. 4
• B. 24
• C. 5
• D. 225

Answer 1

The correct option is D 225

Total cost of $x_1$ component by using standard machine tool

$(TC{)}_1=(\frac{30}{60}+\frac{22x_1}{60})\times 200$

$=100+\frac{2200}{30}{x}_1$

Total cost $x_2$ component by using an Automatic machine tool.

$(TC{)}_2=(2+\frac{5}{60}\times x_2)\times 800$

$=1600+\frac{2000}{30}{x}_2$


Let the break even quantity be x.
At break even point

$(TC{)}_1=(TC{)}_2$

$\therefore 100+\frac{2200}{30}x=1600+\frac{2000}{30}x$

$6.667x=1500$

$\therefore x=225$