The Dura-Bar company is a major producer of cast iron. Its management estimates that the demand for the company's product is given by the equation

Q = 5,000 - 1,000 PC+ 0.1 I + 200 PS,

where:

Q is the quantity of Dura-Bar cast iron demanded in thousands of tons per year.

PCis the price of cast iron in dollars per pound.

I is the income per capita in the region.

PSis the price of steel in dollars per pound.

Initially, the price of cast iron is $1 per pound, income per capita in the region is $45,000, and the price of steel is $0.80 per pound.

1. a)How much cast iron will be demanded at the initial prices and income?
2. b)Are cast iron and steel substitutes or complements?
3. c)If the objective is to maintain the quantity of cast iron demanded as computed in part (a), what reduction in the cast iron price will be necessary to compensate for a $0.20 reduction in the price of steel?