Midland Petroleum is holding a stockholders$$ meeting next month. Ms$.$ Ramsey is the president of the company and has the support of the existing board of directors. All $12$ members of the board are up for reelection. Mr$.$ Clark is a dissident stockholder. He controls proxies for $57,001$ shares. Ms$.$ Ramsey and her friends on the board control $67,001$ shares. Other stockholders, whose loyalties are unknown, will be voting the remaining $24,998$ shares. The company uses cumulative voting.

a$.$ How many directors can Mr$.$ Clark be sure of electing?

Note: Do not round intermediate calculations. Round down your answer to the nearest whole number.

b$.$ How many directors can Ms$.$ Ramsey and her friends be sure of electing?

Note: Do not round intermediate calculations. Round down your answer to the nearest whole number.

c$-1.$ How many directors could Mr$.$ Clark elect if he obtains all the proxies for the uncommitted votes?

Note: Do not round intermediate calculations. Round down your answer to the nearest whole number.

c$-2.$ Will he control the board?

multiple choice

Yes

No

d$.$ If nine directors were to be elected, and Ms$.$ Ramsey and her friends had $83,001$ shares and Mr$.$ Clark had $63,001$ shares plus half the uncommitted votes, how many directors could Mr$.$ Clark elect? Assume the same number of total shares as the original question.

Note: Do not round intermediate calculations. Round down your answer to the nearest whole number.