Consider the following spreadsheet and Excel Solver sensitivity report. $($The profit is in dollars, and the variables x$1$ and x$2$ represent the number of units of products $1$ and $2,$ respectively.$)$

A B C D E

$1$

$2$ Input Information

$3$ x$1$ x$2($type$)$ Avail.

$4$ Constraint $125<42$

$5$ Constraint $231<32$

$6$ Constraint $311>13$

$7$

$8$ Profit $45$

$9$

$10$ Output Information

$11$ Variables

$12$ Profit $=$ Total

$13$

$14$ Resources Used Slack$/$Surplus

$15$ Constraint $1$

$16$ Constraint $2$

$17$ Constraint $3$

$18$

$19$

Sensitivity Report

Variable Cells

Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease

$B$$11$ Variables x$19\mathrm{.}07692307704112$

$C$$11$ Variables x$24\mathrm{.}7692307690553\mathrm{.}666666667$

Constraints

Cell Name Final Value Shadow Price Constraint R$.$H$.$ Side Allowable Increase Allowable Decrease

$B$$15$ Constraint $1$ Used $420\mathrm{.}8461538462421185\mathrm{.}5$

$B$$16$ Constraint $2$ Used $320\mathrm{.}769230769232313\mathrm{.}666666667$

$B$$17$ Constraint $3$ Used $13\mathrm{.}846153850130\mathrm{.}8461538461$E$+30$

Use the spreadsheet and Excel Solver sensitivity report to answer these questions.

$($a$)$

What is the cell formula for B$12($the profit contribution of variable x$1)?$