MATH 340 Midterm: MATH 340 2014 Winter Test 1

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turquoisegnu128

9 Jan 2019

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[8: find the value of alice announces a pure strategy and betty announces a pure strategy for the matrix game. Find the value of the mixed strategy games and the optimal mixed strategies for alice and betty. [10: consider the problem: maximize x1 + 2x2 subject to x1 2x2 4, x1 2x2 7, x1 + x2 1, and x1, x2 0. Write this as a linear program in standard form. Use the two-phase method, adding an auxilliary variable x0 to every slack variable equation in the dictionary, to solve this lp. Use the smallest subscript rule to break any ties for entering or leaving variables. [hint: this should not take more than two or three pivots. ] [6: consider the linear program: maximize s + 10t + r subject to 2s + 5t + r 16, 3s + t 3r 12, 4s + 3t + 3r 20, and t, r 0, but where s can be negative, zero, or positive.

Related Questions

(A) Find the optimal Strategy P*. Hint if a row was deleted,the probability of choosing that row is zero

P* = [ ___ ___ ___ ___] (type fully reduced fractions of mixednumbers.)

Find the optimal Strategy Q*. Hint: if a column was deleted,the probability of choosing that column is zero.

Q*= ____

____

(Type fully reduced fractions or mixed numbers)

What is the value v of the game?

v= ____ (type a fully reduced fraction or mixed number)

(B) What is the expected value of the game for R if the bank Ralways chooses TV and bank C uses its optimum strategy?

E= _____ (type fully reduced fraction or mixed number)

(C) What is the expected value of the game for R if the bank Calways chooses radio and bank R uses its optimum strategy?

E= _____ (type fully reduced fraction or mixed number)

(D) What is the expected value of the game for R if both banksalways use the paper?

E= ____ (Enter an integer or decimal. Round to two decimalplaces)