$x_{i}0$ for $i=1,2,3$

$y_f=0,1$ for $i=1,2,3$

How many total meals will $be$ provided over the year?

$(c)$ What $is$ the solution $ifwe$ add a third category manager and all other available resources stay the same?

$\begin{array}{cc}\text{C}\text{a}\text{t}\text{e}\text{g}\text{o}\text{r}\text{y}& \text{N}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{E}\text{v}\text{e}\text{n}\text{t}\text{s}\\ \text{C}\text{h}\text{u}\text{r}\text{c}\text{h}\text{F}\text{o}\text{o}\text{d}\text{D}\text{r}\text{i}\text{v}\text{e}& ?\\ 5K\text{R}\text{u}\text{n}& ?\\ \text{C}\text{o}\text{n}\text{c}\text{e}\text{r}\text{t}& ?\end{array}$

How many more meals are provided $by$ adding a third$-$category coordinator?Resources Required per Event per Category

Below $is$ the number $of$ meals provided per event for each category and the lower and upper $limiton$ events $in$ the category $if$ that category $is$ chosen.

Max$142000x_1+91000x_2+113100x_3$

$s.t.$

paid staff $(hours)110x_1+145x_2+138x_{5}2000$

volunteer staff $(hours)83x_1+56x_2+227x_{3}1900$

supplies $($$$)500x_1+1500x_2+800x_{S}100000$

minimum church food drives $x_{1}5y_1$

maximum church food drives $x_{1}11y_1$

minimum $5K$ runs $x_{2}2y_2$

maximum $5K$ runs $x_{2}4y_2$

minimum concerts $x_{3}2y_5$

maximum concerts

two categories chosen $y_1+y_2+y_5=2$