Recall the production model:

Max $10$x

s$.$t$.$

$5$x $<=40$

x $>=0$

Suppose the firm in this example considers a second product that has a unit profit of $$5$ and requires $2$ hours of labor time for each unit produced. Use y as the number of units of second product produced.

$($a$)$

Show the mathematical model when both products are considered simultaneously.

Max

s$.$t$.$

x $>=0,$ y $>=0$

$($b$)$

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

$($i$)$

controllable

x

y

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$.)$

No file chosen

This answer has not been graded yet.

$($d$)$

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

x $=$

y $=$

P $=$ $

$($e$)$

Is the model developed in part $($a$)$ a deterministic or a stochastic model? Explain.

The uncontrollable inputs are

$---$Select$---$

and

$---$Select$---$

$,$ so the model is

$---$Select$---$

$.$