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 y as the number of units of product $2$ produced.

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

b$.$ Identify the controllable and uncontrollable inputs for this model.