Consider a cocoa processor who sources cocoa beans from a single supplier using quantity flexibility contract (r,e) where r denotes the unit...

Consider a cocoa processor who sources cocoa beans from a single supplier using quantity flexibility contract (r,e) where r denotes the unit reservation price and e denotes the unit exercise fee. The processor uses the cocoa beans to produce cocoa butter with selling price of $80 per kg. The processing cost is normalized to zero, so the only cost is the procurement cost of the cocoa beans. The processor can source the cocoa beans from the supplier in advance of the spot market and from a spot market on the day. The processor has a spot price forecast w, $ per kg, for cocoa beans with the following scenarios: Scenario A: $100 with probability ¼ Scenario B: $60 with probability ½ Scenario C: $20 with probability ¼

a)    A supplier (Supplier1) is offering the contract (25, 30). Is it profitable to order from this supplier? Why?

b)   There is another supplier (Supplier2) offering the contract (20,25). Which supplier should the processor choose to order from? Why?

c)    What if Supplier2 offers (30,15)? Which supplier should the processor choose to order from? Why?