In a decentralized supply chain with 2 levels: one supplier and one retailer. The demand is given by (100-3*retail_price) units. The product cost is 5 dollars.

If there were only one agent in the supply chain, what would be the retail price to maximize the supply chain profit?

What is the unit price charged by the supplier to maximize the supplier profits, knowing the retailer best response to the supplier price?

If the supplier price to the retailer is 10 dollars per unit. What is the price charged by the retailer (per unit) to maximize retailer profits?

If there were only one agent in the supply chain, what would be the maximum achievable supply chain profit in dollars?