Since the summer is expected to be hot having a lot of sunshine a manufacturer of sun protective lotions needs to decide how many sun protective lotions have to be produced. The sun protective lotions are sold for 6 liras and its production cost is 2 liras. Since the demand is uncertain the manufacturer believes based on previous experience that the random demand D for the sun lotion has the following distribution P(D = 4000) = 0.8, P(D = 5000) = 0.2 The manufacturer can produce any amount q of sun protective lotions and its aim is to maximize its expected profit.

Draw the decision tree of this problem if the manufacturer decides to produce q products and compute its expected profit producing q items if it happens that unsold sun protective lotions have to be thrown away at zero cost. And determine the optimal production quantity.