This question needs to be done with R language programming

A company must decide whether to manufacture a component part in its plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars):

State of Nature

Decision Alternative Low Demand, s₁ Medium Demand,s₂ High Demand,s₃

Manufacture,d₁ -20 40 100

Purchase, d₂ 10 45 70

The state-of-nature probabilities are P(s₁) = 0.35, P(s₂) = 0.35, and P(s₃) = 0.30.

a.Use a decision tree to recommend a decision.

b.A test market study of the potential demand for the product is expected to report either a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:

P(F|s₁) = 0.10P(U|s₁) =0.90

P(F|s₂) = 0.40P(U|s₂) = 0.60

P(F|s₃) = 0.60P(U|s₃) = 0.40

What is the probability that the market research report will be unfavorable?

c.What is the company's optimal decision strategy?

d.What is the expected value of the market research information?