Two operators are required for machine $1$thus$,2$ hours of labor must be scheduled for each hour of machine $1$ time. Only one operator is required for machine $2.$ A maximum of $100$ labor$-$hours is available for assignment to the machines during the coming week. Other production requirements are that product $1$ cannot account for more than $50\%$ of the units produced and that product $3$ must account for at least $20\%$ of the units produced. week. Other production requirements are that product $1$ cannot account for more than $50\%$ of the units produced and that product $3$ must account for at least $20\%$ of the units produced.

$($a$)$ How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit $($in $ $)$ associated with your solution?

Product $1=$

Product $2=$

Product $3=$

weekly profit $ $=$

$($b$)$ How many hours of production time will be scheduled on each machine?

machine $1=\_\_\_\_\_\_\_hr$

machine $2=\_\_\_\_\_\_\_\_hr$

$($c$)$ What is the value $($in $ $)$ of an additional hour of labor?

$ $=$

$($d$)$ Assume that labor capacity can be increased to $160$ hours. Develop the optimal product mix and the projected weekly profit $($in $ $),$ assuming the extra hours are made available.

Product $1=$

Product $2=$

Product $3=$

weekly profit $ $=$

Would you be interested in using the additional $60$ hours available for this resource?

Yes, the weekly profit would be increased. or$,$

No$,$ the weekly profit would be decreased.

Please answer preferably using Solver add$-$in in Excel and show work.