Q$2(1$ point$).$ Mack$$s guitar fabricaTon shop produces low$-$cost$,$ highly durable guitars for beginners. Typically, only $80$ percent of the guitars that begin producTon each month are considered good enough to sell; the other $20$ percent are scrapped due to quality problems that are idenTfied aXer they have completed the producTon process. Each guitar sells for $$300.$ Because some of the producTon process is automated, each guitar only requires $10$ labor hours. Each employee works an average $100$ hours per month, and $5$ employees work in the fabricaTon shop. Labor is paid at $$10/$hour$,$ materials cost is $$40/$guitar$,$ scrap cost is $$5/$guitar$,$ and overhead is $$4,000.$

a$.$ Calculate the mulTfactor and labor producTvity raTos.

b$.$ AXer some study, the operaTons manager Darren Funk recommends three opTons to improve the company$$s mulTfactor producTvity: $(1)$ increase the sales price by $10$ percent, $(2)$ improve quality so that only $10$ percent are defecTve and scrapped aXer the producTon process, or $(3)$ reduce labor, material, scrap, and overhead costs by $10$ percent. Calculate the mulTfactor producTvity raTo for each opTon and determine the opTon that has the greatest impact on the mulTfactor producTvity measure.