A company manufactures two types of smart gadgets: Gadget X and Gadget Y$.$ The company aims to

maximize its profit while adhering to manufacturing, resource, and market constraints. The

company has formulated the following Linear Programming $($LP$)$ model:

Maximize Z $=500$ X $+400$ Y

subject to

$50$ X $+25$ Y $<=300($manufacturing time constraint$)$

$6$ X $+15$ Y $<=60($resource availability constraint$)$

$-$ X $+2$ Y $<=4($production balance constraint$)$