Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all $>=$ constraints.

A B C D E F

$1$ Input Section

$2$ Objective Function Coefficients

$3$ X Y

$476$

$5$

$6$ Constraints Avail.

$7$ #$14357$

$8$ #$22549$

$9$ #$398142$

$10$

$11$ Output Section

$12$

$13$ Variables $611$

$14$ Profit $4266108$

$15$

$16$ Constraint Usage Slack

$17$ #$1570$

$18$ #$26718$

$19$ #$31420$

$20$

$($a$)$

Give the original linear programming problem. $($Write your answer without slack or surplus variables.$)$

Min

s$.$t$.$

Constraint #$1$

Constraint #$2$

Constraint #$3$

X$,$ Y $>=0$

$($b$)$

What are the optimal values of X and Y given in the spreadsheet above.

X $=$

Y $=$