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Question 5 [18 points| An existing warehouse will be used for the storage of 5 product families. The warehouse consists of storage bays of size 20 ft x 20 ft. The percentage of using Dock 1 is 40%, Dock 2 is 30%, Dock 3 is 30%. The area requirement and monthly load rate for each product family are shown in the table below. (You can round up fractional values) Product Family Area Required Load Rate Dock 3 D1 2 3 4 5 3200 3900 1800 2350 2650 1100 2300 500 900 700 Dock 2 (a) (5 points Calculate the expected distance for Cells X. Y and Z (X,Y,Z). (b) [4 points) Assuming the following distance scoring (only for this part of the question), determine the layout that will minimize the total expected travel distance. 5 10 10 15 20 15 10 5 5 10 5 15 20 25 30 25 20 10 10 15 10 15 20 25 30 25 20 15 15 20 15 20 15 10 10 15 20 25 30 25 (c) 14 points Formulate the described problem by using an LP. (d) 15 points Change your LP model (at part c) accordingly. (only state the modified parts) 1- Assume that Product family 3 and 5 cannot be stored next to each. If they are stored next to each other, there will be a cost since all of the stored product 3s will be destroyed. 2- State that If cell 1 is allocated for product 1, cell 10 should be allocated for product 3