In your managerial role overseeing production at Cool Economic Beans, your main product is a line of baked beans, in a market with demand Qb = 12,000 - 40 Pb, where Qb is the quantity of cans of beans sold and Pb is the price of beans per can. Cool Economic Beans faces production costs of TC = 4500 + 100Qb. However, production involves a useful waste product: the shells from each bean can be sold to other companies to produce cat litter at no cost to Cool Economic Beans. Demand for these bean shells is given by: Qs = 6500 - 1000Ps, where Qs refers to the pounds of shells sold at price, Ps, to the other companies. Importantly, the production of each can of beans produces exactly one pound of shells.

1. Do economies of scope exist for beans and shells?
2. What is the optimal number of cans of beans that cool Economic Beans should produce and sell?
3. What is the optimal number of pounds of shells Cool Economic Beans should sell to cat litter producers? At what price should the shells be sold?