QUES: along with two inequality systems expressing economic efficiency. In this model, the (transposed) probability vector p represents the prices of the goods while the probability vector q represents the "intensity" at which the production process would run. The unique solution represents the growth factor which is 1 plus the rate of growth of the economy; the rate of growth equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann.

What is the rate of qrowth equal to?
What is the answer?
ANS: rate of growth equals the interest rate
QUES: Undergraduate tuition for the 2012/13 school year was $61,240; this includes the basic tuition of $43,380, fees (health $200, etc.), room and board of $13,329 (less if commuting), books and supplies $1,842, personal expenses $1,890, transportation cost of $400. Northwestern awards financial aid solely on the basis of need through loans, work-study, grants, and scholarships. The University processed in excess of $472 million in financial aid for the 20092010 academic year. This included $265 million in institutional funds, with the remainder coming from federal and state governments and private organizations and individuals. Northwestern scholarship programs for undergraduate students support needy students from a variety of income and backgrounds. Approximately 44 percent of the June 2010 graduates had received federal and/or private loans for their undergraduate education, graduating with an average debt of $17,200.

What was the total undergrad tuition for the 2015/2016 school year?
What is the answer?
ANS: unanswerable
QUES: Following the glass batch preparation and mixing, the raw materials are transported to the furnace. Soda-lime glass for mass production is melted in gas fired units. Smaller scale furnaces for specialty glasses include electric melters, pot furnaces, and day tanks. After melting, homogenization and refining (removal of bubbles), the glass is formed. Flat glass for windows and similar applications is formed by the float glass process, developed between 1953 and 1957 by Sir Alastair Pilkington and Kenneth Bickerstaff of the UK's Pilkington Brothers, who created a continuous ribbon of glass using a molten tin bath on which the molten glass flows unhindered under the influence of gravity. The top surface of the glass is subjected to nitrogen under pressure to obtain a polished finish. Container glass for common bottles and jars is formed by blowing and pressing methods. This glass is often slightly modified chemically (with more alumina and calcium oxide) for greater water resistance. Further glass forming techniques are summarized in the table Glass forming techniques.

What happens during refining?
What is the answer?
ANS:
removal of bubbles