Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 matchsticks, and Fred goes first. On each turn, each player may remove either one, two, or three matchsticks. The player to remove the last matchstick wins the game. (a) Suppose there are only 5 matchsticks left, and it is Fred’s turn. What move should Fred make to guarantee himself victory? Explain your reasoning.
(b) Suppose there are 10 matchsticks left, and it is Fred’s turn. What move should Fred make to guarantee himself victory?
(c) Now start from the beginning of the game. If both players play optimally, who will win?
(d) What are the optimal strategies (complete plans of action) for each player?
Hope your writing looks readable and please draw the tree if possible.

Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: asset a e(ra) = 18.5% σa = 20% asset b e(rb) = 15% σb = 27% an investor with a risk aversion of a = 3 would find that on a risk-return basis. a. only asset a is acceptable b. only asset b is acceptable c. neither asset a nor asset b is acceptable d. both asset a and asset b are acceptable

Laval produces lamps and home lighting fixtures. its most popular product is a brushed aluminum desk lamp. this lamp is made from components shaped in the fabricating department and assembled in the assembly department. information related to the 22,000 desk lamps produced annually follows.direct materials $280,000direct labor fabricating department (8,000 dlh × $24 per dlh) $192,000assembly department (16,600 dlh × $26 per dlh) $431,600machine hours fabricating department $15,200mhassembly department $20,850mhexpected overhead cost and related data for the two production departments follow.fabricating assemblydirect labor hours 150,000dlh 295,000dlhmachine hours 161,000mh 128,000mhoverhead cost $400,000 430,000required1. determine the plantwide overhead rate for laval using direct labor hours as a base.2. determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.3. compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.4. use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

States that if there is no specific employment contract saying otherwise, the employer or employee may end an employment relationship at any time, regardless of cause. rule of fair treatment due-process policy rule of law employment flexibility employment at will