Question 1173267
Let's break down the information from the linear program output to answer each question:

**a. Player A's Optimal Mixed Strategy**

* **PA1 = 0.050:** Player A should play strategy 1 with a probability of 0.05 (or 5%).
* **PA2 = 0.600:** Player A should play strategy 2 with a probability of 0.60 (or 60%).
* **PA3 = 0.350:** Player A should play strategy 3 with a probability of 0.35 (or 35%).

Therefore, Player A's optimal mixed strategy is (0.05, 0.60, 0.35).

**b. Player B's Optimal Mixed Strategy**

To find Player B's optimal mixed strategy, we look at the **DUAL PRICES** of the constraints. These represent the optimal probabilities for Player B's strategies.

* Constraint 1's Dual Price = -0.500
* Constraint 2's Dual Price = -0.500
* Constraint 3's Dual Price = 0.000

However, the Dual Prices must be converted into positive values, and then normalized, as they represent the negative of the player B's strategy.
Also, the dual prices represent the negative of the player B's strategy, and the 4th constraint represents the gain.
Therefore, the dual prices of constraints 1,2, and 3 are the negative of the probabilities of player B's strategies.

To normalize the dual prices, we must take the absolute value of the dual prices. Then add them together.

0.5 + 0.5 + 0 = 1

Then we can divide each dual price by the sum.

* Player B strategy 1: 0.5/1 = 0.5
* Player B strategy 2: 0.5/1 = 0.5
* Player B strategy 3: 0/1 = 0

Therefore, Player B's optimal mixed strategy is (0.5, 0.5, 0).

**c. Player A's Expected Gain**

* **OBJECTIVE FUNCTION VALUE = 3.500**
* **GAINA = 3.500**

Player A's expected gain is 3.5.

**d. Player B's Expected Loss**

In a zero-sum game, Player B's expected loss is equal to Player A's expected gain.

Therefore, Player B's expected loss is also 3.5.