a$.$ Formulate this problem as a linear, integer, or mixed integer program.

b$.$ Assist Ali 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 Ali 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 was the tank filled over the demand required, and by how much more?

Why do you think this is happening?

g$.$ Assume that the water bill is calculated in a different way as follows: Once the

consumption reaches a specific segment, the cost per m$3$

of that segment is used to

calculate the bill on all water consumed for that specific month. For example, if $50$ m$3$

is

consumed in a month, this means that Ali$$s consumption reached segment# $3.$ The bill

then is equal to $50*4\mathrm{.}00=200$ SR$.$ Modify your formulation to account for this new bill

calculation method. Explain the new decision variables, objective function, and

constraints, if any.

h$.$ In relation to part g$,$ how much water now $($in m$3$

$)$ should Ali fill the water tank for each

of the next $12$ months?