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

$487$

$5$

$6$ Constraints Avail.

$7$ #$14357$

$8$ #$22551$

$9$ #$398145$

$10$

$11$ Output Section

$12$

$13$ Variables $4\mathrm{.}213\mathrm{.}4$

$14$ Profit $33\mathrm{.}693\mathrm{.}8127\mathrm{.}4$

$15$

$16$ Constraint Usage Slack

$17$ #$1570$

$18$ #$275\mathrm{.}424\mathrm{.}4$

$19$ #$31450$

$20$

$($a$)$

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

Min

Correct: Your answer is correct.

s$.$t$.$

Constraint #$1$

Incorrect: Your answer is incorrect.

Constraint #$2$

Incorrect: Your answer is incorrect.

Constraint #$3$

Correct: Your answer is correct.

X$,$ Y $>=0$

$($b$)$

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

X $=$

$4$

Incorrect: Your answer is incorrect.

Y $=$

$7$

Incorrect: Your answer is incorrect.

What is the maximum value?

$33\mathrm{.}6$

Incorrect: Your answer is incorrect.