SleazeCo manufacturers residential air conditioning units in Ohio and sells them in Michigan and in Arizona. These units are fairly unique in that they are very energy efficient and are in demand by households that are concerned about global warming and want to be "green." The demand curve for these units in Michigan is described by , where is the price per unit in thousands of dollars and is the number of units (in thousands). The demand curve in Arizona is described by , where is the price per unit (in thousands) and is the number of units (in thousands). The company produces these in one plant in Ohio that has the following total cost function:
,where is the quantity in thousands and is in thousands. Although Arizona is farther away from Ohio than Michigan is from Ohio, assume the transportation costs (for delivery) is the same and, for simplicity, equal to zero.
Questions:
1. How many units should the company make?
2. What price should it charge in Arizona?
3. What price should it charge in Michigan?
4. What is the profit on these products?