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5) Midco's executives have decided that, considering the business environment, the current expected duration of the project is not competitive. They want to ensure that the probability of completing the project in 8 months (240 days) is at least 80%. By how many days should the expected project duration be shortened? Assume crashing actions do not impact the variance of the activity durations. \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline & & Optimistic & Most Likely & Pessimistic & & Crash & & \\ \hline Activity & Activity ID & Time & Time & Time & Normal Cost & Time & & Crash Cost \\ \hline Issue NPP & N1 & 1 & 3 & 5 & 30,000 & & & \\ \hline Assign product ID number & N2 & 1 & 6 & 9 & 57,700 & & & - \\ \hline Distribute NB samples & N3 & 2 & 9 & 14 & 87,700 & 3 & $ & 101,875 \\ \hline Establish manufacturing feasibility & Pr1 & 5 & 11 & 14 & $106,500 & 4 & $ & \$ 146,800 \\ \hline Manufacturing capacity analysis & Pr2 & 3 & 10 & 13 & 95,400 & & & - \\ \hline Label copy check & R1 & 3 & 7 & 9 & $67,700 & -. & & \\ \hline Issue packaging specs & Pk1 & 5 & 13 & 19 & $127,700 & 4 & $ & $140,705 \\ \hline Generate graphics for text and samples & A1 & 7 & 18 & 23 & $173,000 & 6 & $ & 5214,800 \\ \hline Packaging feasibility check & Pk2 & 3 & 9 & 13 & $87,700 & & & - \\ \hline Packaging capacity check & Pk3 & 2 & 6 & . 11 & 61,200 & & & - \\ \hline Formula development & RD1 & 39 & 76. & 162 & $817,200 & 24 & $ & 1,418,900 \\ \hline Formula stability test & RD2 & 70 & 162 & 284 & $1,655,000 & 40 & $ & 2,607,500 \\ \hline External lab test & E1 & 20 & 41 & 54 & $400,700 & 14 & $ & 567,555 \\ \hline Issue preliminary card & RD3 & 1 & 3 & 5 & $30,000 & & & - \\ \hline Produce marketing samples & Pk4 & 7 & 19 & 29 & $187,700 & 6 & $ & 240,914 \\ \hline Profitability analysis & N4 & 1 & 10 & 21 & $102,400 & -. & & -. \\ \hline Establish price & N5 & 1 & 10 & 18 & $98,900 & - & & - \\ \hline Issue sell sheet & \$1 & 20 & 48 & 57 & $457,900 & 18 & $ & 562,537 \\ \hline Distribute marketing samples & S2 & 14 & 27 & 41 & $271,200 & 13 & $ & 336,382 \\ \hline Final regulatory approval & R2 & 10 & 19 & 22 & $183,000 & 8 & $ & 238,000 \\ \hline Scale up batch & Pr3 & 14 & 22 & 27 & $216,500 & 10 & $ & 236,625 \\ \hline Issue manufacturing card & RD4 & 2 & 7 & 9 & $66,500 & & & - \\ \hline Validation control & QC1 & 7 & 19 & 23 & $180,700 & 6 & $ & 241,384 \\ \hline Initiate first packaging and production run & & 7 & 17 & 29 & $172,400 & 5 & $ & 214,322 \\ \hline \end{tabular} 5) Midco's executives have decided that, considering the business environment, the current expected duration of the project is not competitive. They want to ensure that the probability of completing the project in 8 months (240 days) is at least 80%. By how many days should the expected project duration be shortened? Assume crashing actions do not impact the variance of the activity durations. \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline & & Optimistic & Most Likely & Pessimistic & & Crash & & \\ \hline Activity & Activity ID & Time & Time & Time & Normal Cost & Time & & Crash Cost \\ \hline Issue NPP & N1 & 1 & 3 & 5 & 30,000 & & & \\ \hline Assign product ID number & N2 & 1 & 6 & 9 & 57,700 & & & - \\ \hline Distribute NB samples & N3 & 2 & 9 & 14 & 87,700 & 3 & $ & 101,875 \\ \hline Establish manufacturing feasibility & Pr1 & 5 & 11 & 14 & $106,500 & 4 & $ & \$ 146,800 \\ \hline Manufacturing capacity analysis & Pr2 & 3 & 10 & 13 & 95,400 & & & - \\ \hline Label copy check & R1 & 3 & 7 & 9 & $67,700 & -. & & \\ \hline Issue packaging specs & Pk1 & 5 & 13 & 19 & $127,700 & 4 & $ & $140,705 \\ \hline Generate graphics for text and samples & A1 & 7 & 18 & 23 & $173,000 & 6 & $ & 5214,800 \\ \hline Packaging feasibility check & Pk2 & 3 & 9 & 13 & $87,700 & & & - \\ \hline Packaging capacity check & Pk3 & 2 & 6 & . 11 & 61,200 & & & - \\ \hline Formula development & RD1 & 39 & 76. & 162 & $817,200 & 24 & $ & 1,418,900 \\ \hline Formula stability test & RD2 & 70 & 162 & 284 & $1,655,000 & 40 & $ & 2,607,500 \\ \hline External lab test & E1 & 20 & 41 & 54 & $400,700 & 14 & $ & 567,555 \\ \hline Issue preliminary card & RD3 & 1 & 3 & 5 & $30,000 & & & - \\ \hline Produce marketing samples & Pk4 & 7 & 19 & 29 & $187,700 & 6 & $ & 240,914 \\ \hline Profitability analysis & N4 & 1 & 10 & 21 & $102,400 & -. & & -. \\ \hline Establish price & N5 & 1 & 10 & 18 & $98,900 & - & & - \\ \hline Issue sell sheet & \$1 & 20 & 48 & 57 & $457,900 & 18 & $ & 562,537 \\ \hline Distribute marketing samples & S2 & 14 & 27 & 41 & $271,200 & 13 & $ & 336,382 \\ \hline Final regulatory approval & R2 & 10 & 19 & 22 & $183,000 & 8 & $ & 238,000 \\ \hline Scale up batch & Pr3 & 14 & 22 & 27 & $216,500 & 10 & $ & 236,625 \\ \hline Issue manufacturing card & RD4 & 2 & 7 & 9 & $66,500 & & & - \\ \hline Validation control & QC1 & 7 & 19 & 23 & $180,700 & 6 & $ & 241,384 \\ \hline Initiate first packaging and production run & & 7 & 17 & 29 & $172,400 & 5 & $ & 214,322 \\ \hline \end{tabular}