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 $125<44$

$5$ Constraint $231<34$

$6$ Constraint $311>11$

$7$

$8$ Profit $65$

$9$

$10$ 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$19\mathrm{.}6923076920694$

$C$$11$ Variables x$24\mathrm{.}92307692305103$

Constraints

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

$B$$15$ Constraint $1$ Used $440\mathrm{.}69230769234412621\mathrm{.}333333333$

$B$$16$ Constraint $2$ Used $341\mathrm{.}538461538343215\mathrm{.}666666667$

$B$$17$ Constraint $3$ Used $14\mathrm{.}615384620113\mathrm{.}6153846151$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$1)?$

$=$SUM$($B$4$:B$6)*$B$11$

$=$SUM$($B$4$:B$6)*$B$8$

$=$B$8$ B$11$

$=$B$8*$B$11$

$=$SUM$($B$4$:B$6)$ B$11$