To make a given part interchangeable, it was necessary to reduce the tolerance

on the outside diameter from $+-0\mathrm{.}010$ to $+-0\mathrm{.}005$ at a resulting cost increase of

$50$ percent of the turning operation. The turning operation represented $20$ percent of

the total cost. Making the part interchangeable meant that the volume of this part

could be increased by $30$ percent. The increase in volume would permit production

at $90$ percent of the former cost. Should the methods engineer proceed with the

tolerance change? Explain.