Consider the following demand scenario:

Quantity

Probability $(\%)$

$2,000$

$3$

$2,100$

$8$

$2,200$

$15$

$2,300$

$30$

$2,400$

$17$

$2,500$

$12$

$2,600$

$10$

$2,700$

$5$

Suppose the manufacturer produces at a cost of Rs$.20$ per unit. The distributor sells to end customers for Rs$.50$ per unit during the season and unsold units are sold for Rs$.10$ per unit after the season.

$($a$)$ What is the system's optimal production quantity under global optimisation?

$($b$)$ Suppose the manufacturer produces make$-$to$-$order units and sells to the distributor at Rs$.40$ per unit. What is the expected profit?

$($c$)$ Explore and write a note on the various contractual options covered in the video for make$-$to$-$order supply chainConsider the following demand scenario $.$ Please refer to the attached image for table