Question: Since the summer is expected to be hot having a lot of sunshine a manufacturer of sun pro- tective lotions needs to decide how many

Since the summer is expected to be hot having a

Since the summer is expected to be hot having a lot of sunshine a manufacturer of sun pro- tective 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 un- certain 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 of sun protective lotions and its aim is to maximize its expected profit. 1. (8 points) 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. 2. (6 points) Determine the optimal production quantity. 3. (6 points) Fortunately it turns out that the unsold sun protective lotions can be sold to an outlet at the price of 1.5 lira. What does change in the optimal production quantity? Explain your answer. Since the summer is expected to be hot having a lot of sunshine a manufacturer of sun pro- tective 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 un- certain 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 of sun protective lotions and its aim is to maximize its expected profit. 1. (8 points) 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. 2. (6 points) Determine the optimal production quantity. 3. (6 points) Fortunately it turns out that the unsold sun protective lotions can be sold to an outlet at the price of 1.5 lira. What does change in the optimal production quantity? Explain your

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