A shipping company handles containers in three different sizes: 1. 27 ft^3 (3 × 3 × 3) 2. 125 ft^3 3. 512 ft^3. Let Xi (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With μi = E(Xi) and σi2 = V(Xi), suppose that the mean values and standard deviations are as follows:μ1= 220 μ2=260 μ3=110 μ1=220 μ2=260 μ3=110σ1=11 σ2=12 σ3=6 σ1=11 σ2=12 σ3=6Required:Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped.

In each of the cases below, assume division x has a product that can be sold either to outside customers or to division y of the same company for use in its production process. the managers of the divisions are evaluated based on their divisional profits. case a b division x: capacity in units 200,000 200,000 number of units being sold to outside customers 200,000 160,000 selling price per unit to outside customers $ 90 $ 75 variable costs per unit $ 70 $ 60 fixed costs per unit (based on capacity) $ 13 $ 8 division y: number of units needed for production 40,000 40,000 purchase price per unit now being paid to an outside supplier $ 86 $ 74 required: 1. refer to the data in case a above. assume in this case that $3 per unit in variable selling costs can be avoided on intracompany sales. a. what is the lowest acceptable transfer price from the perspective of the selling division? b. what is the highest acceptable transfer price from the perspective of the buying division? c. what is the range of acceptable transfer prices (if any) between the two divisions? if the managers are free to negotiate and make decisions on their own, will a transfer probably take place?