$(4$ points$)$ The precedence diagram network for a project is shown below, along with the optimistic $(T_o),$ most likely $(T_m),$ and pessimistic $(T_p)$ durations for each activity. Use the PERT process to determine the probability $($in percent$)$ of completing the project in $50$ days or less.

${}_o,T_m,T_p$

$(4$ points$)$ After construction of the formwork for $30$ precast concrete girders started, the durations to construct the formwork for the first two girders on the project were as follows:

Girder $1$: $7\mathrm{.}5$ hours

Girder $2$: $6\mathrm{.}3$ hours

Using an improvement rate based on individual units, answer the following questions:

a$.$ What is the rate of improvement $()?$

b$.$ How long $($in hours$)$ will it take construct the formwork for the ${30}^{th}$ girder? $(T_{30})$

c$.$ In an attempt to accelerate the schedule, the contractor plans to ask the formwork crew to work $11$ hours per day for $5\mathrm{.}5$ days a week. What will be the time required $($hours$)$ to construct the formwork for the ${30}^{th}$ girder with the impact of overtime included?

$6.(3$ points$)$ Based on data from prior projects, the cumulative average time to design the formwork for $10$ precast concrete girders is $3\mathrm{.}75$ hours per girder with an engineer's rate of learning $()$ of $0\mathrm{.}875$ when designing formwork. Assume no impacts of working overtime.

a$.$ What will be the average time per girder that is required to design the formwork for all $28$ girders? $(A_{28})$

b$.$ What will be the total time required to design the formwork for all $28$ girders? $(T_{1-28})$