In 2015, the country of Sorbet was suffering from a period of high unemployment. The new president, Gelato, appointed Sherrie Sherbert as his chief economist. Ms. Sherbert and her staff estimated these supply and demand curves for labor from data obtained from the secretary of labor, Jerry Benjamin:
Q_D = 175 - 4W
Q_S = 16W - 30
where Q is the quantity of labor supplied/demanded in millions of workers and W is the wage rate in scoops, the currency of Sorbet. 

a. Currently, the law in Sorbet says that no worker shall be paid less than 12 scoops per hour. Estimate the quantity of labor supplied, the number of unemployed, and the unemployment rate.
b. President Gelato, over the objection of Secretary Benjamin, has recommended to Congress that the law be changed to allow the wage rate to be determined in the market. If such a law was passed and the market adjusted quickly, what would happen to total employment, the size of the labor force, and the unemployment rate? Show the results graphically.
c. Will the Sorbet labor market adjust quickly to such a change in the law? Why or why not?