Operations Research Answers

Player A and B play a game in which each has three coins, a 5p, 10p and a 20p.
Each selects a coin without the knowledge of the other’s choice. If the sum of the
coins is an odd amount, then A wins B’s coin. But, if the sum is even, then B wins
A’s coin. Find the best strategy for each player and the values of the game.

Player A and B, each take out one or two matches and guess how many matches the
opponent has taken. If one of the players guesses correctly, then the loser has to pay
him as many rupees as the sum of the number held by both players. Otherwise, the
pay out is zero. Write down the payoff matrix and obtain the optimal strategies of
both players.

An advertising agency whishes to reach two types of audiences: customers with
annual income greater than one lakh rupees (target audience A) and customers
with annual income of less than one lakh rupees (target audience B). The total
advertising budget is ` 2,00,000. One programme of TV advertising costs ` 50,000;
one programme of radio advertising costs ` 20,000. For contract reasons, at least
three programmes should to be on TV and the number of radio programmes must be
limited to 5. Surveys indicate that a single TV programme reaches 4,50,000
propective customers in target audience A and 50,000 in target audience B. One
radio programme reaches 20,000 prospective customers in target audience A and
80,000 in target audience B. Formulate it as a LPP and solve it graphically to
maximize the total reach for the programmes.

THE MEANS IN WHICH PEOPLE FIND THE RIGHT WAY TO ACHIEVE THEIR OBJECTIVES IS KNOWN AS

Solve the following LP problem using the two-phase simplex method.

Manimize Z=X1-X2-3X3

Subjects to constraints
-2X1+2X2+3X3=2

2X1+3X2+4X3=1
And
X1, X2, X3≥0

A cassette player repairman finds that the time spent on his job has an exponential distribution
with mean 15 min. If he repairs sets in the order in which they came in, and if the arrival of sets
is approximately Poisson with an average rate of 18 per 9 hours a day, what is repairman’s
expected idle time each day? How many jobs are ahead of the set just brought in?

State true or false and give reasons

i)The set of all convex combinations of a finite number of points X1, X2,...... Xn is not a convex set.

ii) If the pay-off matrix of a game is transformed, saddle point of the game if it exists, changes.

iii) If a negative value appears in the solution values(Xb) column of the simplex method, then the basic solution is optimum

iv) In an assignment problem, if a constant is added to each element of the matrix, the optimal assignment does not change.

v) In an LPP, every feasible solution is optimal.

Player A and B play a game in which each has three coins, a 5p, 10p and a 20p. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, then A wins B’s coin. But, if the sum is even, then B wins A’s coin. Find the best strategy for each player and the values of the game.

Player A and B, each take out one or two matches and guess how many matches the opponent has taken. If one of the players guesses correctly, then the loser has to pay him as many rupees as the sum of the number held by both players. Otherwise, the pay out is zero. Write down the payoff matrix and obtain the optimal strategies of both players.

V = xy+ λ(2,000-20x-10y)
where λ is the Lagrange multiplier.
Now, the first-order conditions for constrained output maximisation are
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