Question $3[14$ pts$]($a$)[4$ pt$]$ If the length of the critical path is $40$ minutes and the average waiting time in the system is $10$ minutes, determine the system$$s:

i$.$ theoretical flow time $($TFT$)=$

ii$.$ average flow time $($T$)=$

iii. flow time efficiency $=$

iv$.$ What should the average waiting time be in order to have a flow time efficiency of $90\%?$

$($b$)[2$ pt$]$ Describe the bullwhip effect in a precise and brief manner.

$($c$)[2$ pt$]$ Does panic ordering impact the bullwhip effect? If yes, briefly explain how $($e$.$g$.,$ increase or decrease?$)$ and why.

$($d$)[6$ pt$]$ Consider the Burrito Game and its facility location type formulation. Suppose there are $5$ potential sites for burrito trucks $($i$.$e$.,$ the blue circles$).$

i$.$ Describe the decision variables $($i$.$e$.,$ variables to change on Excel Solver$).$

ii$.$ How many decision variables does your formulation have?

iii. You decide to use only two trucks, which you locate at sites $1$ and $3.$ Provide the values of the decision variables for this solution.

iv$.$ Does this facility location problem have the total unimodularity property, and if so$,$ what are the practical implications of this property?