Recall the production model from Section $1\mathrm{.}3$:

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 for each unit produced. Assume total production capacity remains $40$ units. Use $yas$ the number $of$ units $of$ product $2$ produced.

Show the mathematical model when both products are considered simultaneously.

HIDE ANSWER

Max

$10$

$x$

$+$

$5$

$y$

$s.t.$

$*$

$5$

$x$

$+$

$2$

$y$

$$

$40$

$*$

$x$

$$

$0$

$,$

$y$

$$

$0$

Identify the controllable and uncontrollable inputs for this model.

HIDE ANSWER

Controllable inputs: $x$ and $y$

Uncontrollable inputs: profit $(10,5),$ labor$-$hours $(5,2),$ and labor$-$hour availability $(40)$