In the structure shown, $15mm$ diameter phin is iused at A and the cable $BD$ has a diancter of $10mm.$ The ultimate shearing stress for the pin at $A$ is $100$MPa and ultimate normal stress for the cable is $140$MPa. For factor of safety of $2\mathrm{.}5,$ determine

$($a$)$ The allowable force $P$ that can be applied

$($b$)$ Explain, with a logical reason, why the allowablo value is a maximum$/$minimum$?$

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