Y=80

Question 5 (4 points) (Replace Y in the question with its value in the table of page 2.) A supermarket sells two types of toy cars (type I and type II). The unit price for type I toy car is $150 and for type II toy car is $180. The unit costs for type I and type II toy cars are $80 and $100, respectively, and the salvage values are $20 and $30, respectively. The monthly demands of the two types of toy cars are independent, and the relative frequencies of monthly demand are listed in the following table. There is a rack used to display the toy cars with the capacity of 4 toy cars. Suppose that only the toy cars displayed on the rack can be purchased by customers. Table 5.1: Monthly demand of two types of toy cars Type I toy car Type II toy car Demand Relative frequency Demand Relative frequency 2 0.1 0 0.05 3 0.15 1 0.05 4 0.15 2 0.2 5 0.4 3 0.3 6 0.15 4 0.3 7 0.05 5 0.1 Q5.1 How many type I toy cars and how many type II toy cars should be displayed on the rack to maximize the expected total profit of the two types of toy cars? (2 points) Q5.2 The supermarket will sell a new type of toy cars (type III) with the unit price of $200, the unit cost of $115, and the salvage value of $35. The monthly demand distribution of type III toy cars is as follows the monthly demand distribution for type I and type II toy cars will not change). Table 5.2: Monthly demand of type III toy cars Type III toy car Demand Relative frequency 1 0.1 2 0.2 3 0.3 4 0.25 5 0.15 A new display rack will be rented (both the old display rack and the new display rack will be used). The capacity and the rent for a new display rack is shown in Table 5.3. Table 5.3: Capacity and rent of a new display rack Display rack Capacity (toy car) Rent per month ($) R1 4 50 R2 5 Y R3 6 95 Which display rack should be rented? How many type I, type II and type III toy cars should be displayed on the two racks (the old one owned by the supermarket and the new one rented)? (2 points)