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St George$$s Craft Brewery is a brewhouse that produces $1200$L batches of beer, averaging $2\mathrm{.}5$ batches produced and distributed per week. All of their beer is packaged in kegs for direct distribution to local restaurants and bars.

When the brewery started up$,$ the founders decided that to minimize the number of kegs that they need to handle, they would use $50$L kegs. During packaging, kegs are filled at ground level. Over the course of the week, they are loaded manually onto the bed of a pickup truck. The truck bed sits $80$cm above ground level.

Additional data:

While the specific gravity and thus weight of beer varies somewhat by type, $50$L of their most popular beer weighs $51$ kg$.$

The keg mass and dimensions are given in the attached specification from Lawson Kegs Inc.

Please make and state any additional assumptions necessary to complete the analyses below.

Using the NIOSH Lifting Equation, calculate the RWL and LI for lifting kegs onto the back of the pickup truck. $[5$ marks$]$

According to this analysis, is the lift safe?

What keg weight would result in an LI of $1?$