You run a bottling company that has the local monopoly on Jolt Cola. You have two plants, each of which has an upward-sloping marginal cost and is...

You run a bottling company that has the local monopoly on Jolt Cola. You have two plants, each of which has an upward-sloping marginal cost and is operating to supply this market. Define your profit maximization problem and explain (using both algebra and graph) the (first-order) conditions that determine

a) how much is supplied by each plant

b) how much soda is supplied to the market overall