$(50$ points$)$ The Widget Maker Company is bidding for a new job that requires building

four widget prototypes. The company has never built the particular widget before, but

its experts believe that its designers and workers will be able to pick it up with a learning

rate of $80\%.$ The activity of designing and building prototypes will gain from this

learning rate for at least five cycles. The proposal team has come up with the following

action plan and effort estimates for producing the four units.

The company plans its work assuming a $90\%$ efficiency of its staff members. Task $2,$ Design

framework, and Task $14,$ Update design knowledge base, require an expert designer who is

available only $50\%$ of the time due to other commitments.

The company has an average labor rate of $$\frac{50}{?}$ hour. The benefit rate is $30\%.$ Its overhead costs

are $50\%$ and its profit margin is $20\%.$ The project plans are to be developed assuming $8$ hours

per working day and $5$ working days per week.