# Optimal Price and Quantity from Inverse Demand and Cost

Al Ain Dairy has reported that its annual sales on dairy products have increased by 20 percent, driven primarily by a 40 percent increase in the demand for camel milk. The increase was largely attributed to a news report describing the health benefits of camel milk. You are the manager of a rival dairy farm that sells camels milk in small bottle of 250ml and you would like to know the optimal number of bottles to sell in a single package. Suppose a typical consumer's inverse demand for you camel milk is P = 11-2Q. If your cost of producing camel's milk is C(Q) = Q, determine the optimal number of bottles to sell in a single package and the optimal package price.

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#### Solution Preview

Revenue = P*Q We are given P in the inverse demand. This sets up the problem as:

Revenue = Q(11-2Q)

= 11Q-2Q^2

The derivative of Revenue is Marginal Revenue.

MR=11-4Q

Cost = C(Q) = Q

The ...

#### Solution Summary

Using inverse demand and cost functions, optimal price and quantity are determined. The problem is shown with explanations for each step.