Use a graphing calculator or a computer program for the simplex method to solve this linear programming problem.

x $1$

x $2$

x $3$

x $4$

s $1$

s $2$

s $3$

$0$

$0$

$\mathrm{.}375$

$\mathrm{.}625$

$1$

$0$

$0$

$500$

$0$

$\mathrm{.}75$

$\mathrm{.}5$

$\mathrm{.}375$

$0$

$1$

$0$

$600$

$1$

$\mathrm{.}25$

$\mathrm{.}125$

$0$

$0$

$0$

$1$

$270$

negative $110$

negative $85$

negative $75$

negative $65$

$0$

$0$

$0$

$0$

Question content area bottom

Part $1$

The optimal solution x $1$

equalsenter your response here$,$

x $2$

equalsenter your response here$,$

x $3$

equalsenter your response here$,$

and x $4$

equalsenter your response here

produces the maximum value enter your response here

$.$

$($Do not round until the final answer. Then round to the nearest integer as$$ needed.$)$