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 to make-to-order in supply chains.