This assignment needs to be done under R language

1.Video Tech is considering marketing one of two new video games for the coming Holiday season¹: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand are as follows:

Demand

Battle Pacific High Medium Low

Profit $1000 $700 $300

Probability 0.2 0.5 0.3

Video Tech is optimistic about its Space Pirates game. However, the concern is that profitability will be affected by a competitor's introduction of a video game viewed as similar to Space Pirates. Estimated profits (in thousands of dollars) with and without competition are as follows:

Space Priates Demand

With competition High Medium Low

Profit $800 $400 $200

Probability 0.3 0.4 0.3

Space Priates Demand

Without competition High Medium Low

Profit $1600 $800 $400

Probability 0.5 0.3 0.2

For planning purposes, Video Tech believes there is a 0.6 probability that its competitor will produce a new game similar to Space Pirates. Given this probability of competition, the director of planning recommends marketing the Battle Pacific video game. Using expected value, what is your recommended decision and what is the expected profit?

2.Reconsider the problem in Question 1. Suppose that the profits (in thousands of dollars) are uncertain.

For Battle Pacific:

When demand is high, the profit is normally distributed with mean 1000 and standard deviation 100.

When demand is medium, the profit is normally distributed with mean 700 and standard deviation 70.

When demand is low, the profit is normally distributed with mean 300 and standard deviation 30.

100.

When demand is medium, the profit is normally distributed with mean 700 and standard deviation 70.

When demand is low, the profit is normally distributed with mean 300 and standard deviation 30.

For Space Pirates with competition:

When demand is high, the profit is normally distributed with mean 800 and standard deviation 80.

When demand is medium, the profit is normally distributed with mean 400 and standard deviation 40.

When demand is low, the profit is normally distributed with mean 200 and standard deviation 20.

For Space Pirates without competition:

When demand is high, the profit is normally distributed with mean 1600 and standard deviation 160.

When demand is medium, the profit is normally distributed with mean 800 and standard deviation 80.

When demand is low, the profit is normally distributed with mean 400 and standard deviation 40.

Incorporate this information to your decision tree. What is the probability that the expected profit will be less than $724.000?