Steel was once rare and expensive, which limited its use to small items like knives. Technological innovations in steel production processes increased the total factor produc- tivity by orders of magnitude, so steel is the most widely used metal today. Maj or inno- vations include the Bessemer process (1857), the Siemens-Martin and Basic Oxygen pro- cesses (early 20th century). Mills using these processes are called \"integrated\" steel mills. After World War II, the U.S. became the world's largest producer of steel, with approxi- mately 39 large, highly capital-intensive integrated steel mills in operation by 1968 in the U.S. supplying a highly competitive global market. Each integrated steel mill could pro- duce steel at a total cost in dollars per ton of TC(q) = 498 + 28q + 78:12 where q is in millions of tons of steel produced per year, and 498 is the annual amortized xed cost. (Note: no unit conversions are needed; use numbers as given.) Total annual demand in tons for U.S. steel in 1968 was Q = 200 0.2P where P is the price per ton in dollars and Q is millions of tons. a. The total aggregate demand for U.S. steel in 1968 was million tons, sold at $ per ton. Each steel mill earned $ prot. The introduction of the Electric-Arc Mini-Mill technology by Nucor Steel in 1969 dis- rupted the industry yet again by improving process efciency using smaller mills with lower capital cost. These mills each had a total annual production cost of TC(q) = 112.5 + 20:; + 200q2 A total of 113 Mini-Mills were operating. By 2019, the industry reached long-run levels. Operators of the 39 older integrated steel mills had to decide whether to shutdown or con- tinue operating. b. There were (number) of integrated mills operating in addition to the Mini-Mills. The total aggregate demand for U.S. steel in 2019 was mil- lion tons, sold at $ per ton