Doc$$s supplier is also considering offering him a buyback contract with the same wholesale price.

$(3$ points$)$ What is the optimal buyback amount $($i$.$e$.,$ b$)?$

Response: the optimal payback amount is $ $\_\_\_\_\_\_\_\_\_$

Detailed calculations

$(3$ points$)$ What is Doc$$s expected profit with the buyback contract?

Response: the expected profit is $ $\_\_\_\_\_\_\_\_\_$ profit

Detailed calculations