A local market research firm has just won a contract for several thousand small projects involving data gathering and statistical analysis. In the past, the firm has assigned each project to a single member of its highly trained professional staff. This person would both gather and analyze the data. Using this approach, an experienced person can complete an average of $10$ such projects in an eight$-$hour day.

The firm$$s management is thinking of assigning two people to each project in order to allow them to specialize and become more efficient. The process would require the data gatherer to fill out a matrix on the computer, check it$,$ and transmit it to the statistical analysis program for the analyst to complete. Data can be gathered on one project while the analysis is being completed on another, but the analysis must be complete before the statistical analysis program can accept the new data. After some practice, the new process can be completed with a standard time of $20$ minutes for the data gathering and $30$ minutes for the analysis.

a$-1.$ What is the production $($output per hour$)$ for each alternative?

Note: Round your answers to $2$ decimal places.

a$-2.$ What is the productivity $($output per labor hour$)$ for each alternative?

Note: Round your answers to $2$ decimal places.

b$-1.$ How long would it take to complete $1,000$ projects with each alternative?

b$-2.$ What would be the labor content $($total number of labor hours$)$ for $1,000$ projects for each alternative?