a. Formulate this problem as a linear program. b. Assist Saeed in determining the monthly amount he should fill in his water tank for the next 12 months. c. What is the total overall cost? d. How much savings can Saeed make over all the 12 months by adopting your model compared to the old method mentioned? e. Indicate the number of times the water bill reached each of the payment segments. f. How many times the tank had to be filled over the demand required, and by how much more? Why do you think this happened? g. Assume that the water bill is calculated in a different way as follows: Once the consumption reaches a specific segment, the cost per m3 of that segment is used to calculate the bill on all water consumed for that specific month. For example, if 50 m3 is consumed in a month, this means that Saeeds consumption reached segment# 4. The bill then is equal to 50*6 = 300 SR. Modify your formulation to account for this new bill calculation method. h. In relation to part d, how much water now (in m3) should Saeed fill his water tank with for each of the next 12 months?

1 3 4 9 Saeed is a homeowner who has been struggling with managing his finances. His utility monthly bills are very high, and he wants to do something about it. His water bill, in particular, is very expensive. He investigated how his water bill is being calculated by the government, and his findings are summarized in Table 1. Table 1 Segment # Water Consumption Price per m (in m) (in SR) 1-15 0.15 2 16 - 30 1.50 31 - 45 4.5 46 - 60 6 5 61 or more The house has a water tank that can hold up to 100 m? On the first day of each month, the tank is filled completely once, and it cannot be filled again until the beginning of the next month. The water meter registers the consumption as soon as the water flows through the pipes into the water tank. Saeed thinks that if he can control the amount of water entering the tank each month, he can minimize his water monthly bill. His family's expected consumption of water for the next year is given in Table 2. Table 2 2022 Month Demand (in m) January February March April May June July August September October 39 November December 21 49 77 34 92 51 38 47 40 20 52 Currently, the water tank is holding 30 mof water. The installed water meter measures to the nearest m. Do the following: 1 3 4 9 Saeed is a homeowner who has been struggling with managing his finances. His utility monthly bills are very high, and he wants to do something about it. His water bill, in particular, is very expensive. He investigated how his water bill is being calculated by the government, and his findings are summarized in Table 1. Table 1 Segment # Water Consumption Price per m (in m) (in SR) 1-15 0.15 2 16 - 30 1.50 31 - 45 4.5 46 - 60 6 5 61 or more The house has a water tank that can hold up to 100 m? On the first day of each month, the tank is filled completely once, and it cannot be filled again until the beginning of the next month. The water meter registers the consumption as soon as the water flows through the pipes into the water tank. Saeed thinks that if he can control the amount of water entering the tank each month, he can minimize his water monthly bill. His family's expected consumption of water for the next year is given in Table 2. Table 2 2022 Month Demand (in m) January February March April May June July August September October 39 November December 21 49 77 34 92 51 38 47 40 20 52 Currently, the water tank is holding 30 mof water. The installed water meter measures to the nearest m. Do the following