Consider a two-echelon supply chain with a manufacturer and a distributor. The table shows the demand distribution.

Quantity	15	16	17	18	19	20	21
Probability	0.02	0.07	0.14	0.36	0.17	0.13	0.11

The manufacturer incurs $22/unit towards the cost of manufacturing. The distributor sells the product to end-users (customers) for $62/unit. The salvage value of unsold items at the end of the selling season is $10/unit. In case of product shortage, each unmet demand receives a coupon for $5. This coupon enables parties to retain customers; otherwise, customers may switch to other distributors. Manufacturers also give coupons of $5/unit whenever the manufacturer fails to fulfill the distributors orders.

2. Assume that the partners are deciding in favor of their interests. Suppose the manufacturer sells to the distributor at $47/unit. How much will the distributor order? What is the expected profit for the manufacturer and distributor?

Diagram to depict when both the partners act in silos (separately) (22 marks) manufacturer and also for distributers

Manufacturer

D

E

M

A

N

D

Probability

Expected profit

O

R

D

E

R

E

D

Manufacturers optimum production units are _______

Manufacturers maximum expected profit (also called optimum) is $______

3. Compare the profits of partners (when silos and collaborate) using a diagram depicting profit lines. Explain briefly what the profit lines infer. How much additional profits, the partners can earn if they collaborate?