Recall the production model:

Max $10x,$

$s.t.$

$,5x40$

$x,0$

$($a$)$ Show the mathematical model when both products are considered simultaneously.

Max

s$.$t$.$

$x0,y0$

$($b$)$ Identify the controllable and uncontrollable inputs for this model. $($Select all that apply.$)$

$(1)$ controllable

$xy$

labor hours

labor availability

unit profit

$($ii$)$ uncontrollable

$x$

$y$

labor hours

labor availability

unit profit

$($c$)$ Draw the flowchart of the input$-$output process for this model. $($Submit a file with a maximum size of $1$ MB$.)$

Choose File no file selected

$($d$)$ What are the optimal solution values of $x$ and $y?($Let $P$ be total profit in dollars.$)$

$x=$

$y=$

$p=$$