Problem $6(20$ points$).$ iScoot Motors Company needs to determine the scooter production quantities for

the next four quarters. The demand during the four quarters is expected to be $d_1=80,d_2=120,d_3=$

$150,d_4=50$ scooters, respectively. At the beginning of the first quarter, the company has an inventory of $20$

scooters. The company can make up to $80$ scooters per quarter using regular$-$time labor at $$800$ per scooter.

Additional scooter can' be made using overtime labor costing $$900$ per scooter. A holding cost of unsold

units is $$40$ per scooter, charged at the end of each quarter. Formulate a linear program for determining a

production schedule that would minimize the total costs of the company during the next four quarters.

Hint: consider the inventory example we see in the class.