$($a$)$ What is the optimal production schedule? What is the number of cars held in inventory

each week, if any?

$($b$)$ The workers$$ union representative announces that they are willing to increase the weekly

overwork capacity by $10$ cars, to a total of $40$ cars per week, for a fixed payment of $$9,000.$

Should Nissan take the deal?

$($c$)$ Without resolving, what is the largest fixed payment such that the workers$$ union pro$-$

posal is profitable for Nissan? Can you guess in which weeks would the extra overwork