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Part $1$

Solve the linear programming problem.

Maximize

z equals $15$ x plus $15$ y

subject to

$8$ x plus $10$ y

greater than or equals$160$

$15$ x minus $12$ y

greater than or equals$54$

x plus y

less than or equals$45$

x

greater than or equals$0$

y

greater than or equals$0.$ What is the maximum value of$$ z$?$ Select the correct choice below$$ and, if$$ necessary, fill in the answer box to complete your choice. At what corner$$ point$($s$)$ does the maximum value of z$$ occur? Select the correct choice below$$ and, if$$ necessary, fill in the answer box to complete your choice.