Instead of already having a given amount of A and B$,$ we start with no inventory but have $$100$ to spend to

purchase A and B$,$ where the prices are: A $=$ $$0\mathrm{.}25/$mol and B $=$ $$0\mathrm{.}5/$mol$.$

The question is how much X$,$ Y$,$ and Z are to be produced to maximize profit $($only costs of reactants are

to be considered, there are no other costs to be factored in$).$

a$)$ Write down an objective function and the constraints above in terms of equalities and$/$or inequalities.

b$)$ Solve the problem using Excel$$s Solver $($or any other solver$).$ Include a clear screenshot of your work,

including the specifications for your solver. Does the solution make sense? Could we have figured out

the optimal solution ourselves instead of using an optimization solver?

c$)$ Suppose additional constraints are given:

If A purchased is more than or equal to B purchased $($in numbers of moles$),$ Z must be produced

at a quantity more than or equal to Y

If more B is purchased than A$,$ at least $25\%$ of the total product must be Y$.$

Write down the constraints above in MILP representation involving binary variables.

Hint: You should be able to use only $3$ binary variables. A $>=$ B is just the opposite of B $>$ A$.$

Solve the problem using Excel$$s Solver $($or any other solver$).$ Include a clear screenshot of your work,

including the specifications for your solver. Discuss the optimal solution compared to what you had in

part b$).$

d$)$ Due to a superstitious manager$$s demand, an additional constraint is given that X$,$ Y$,$ and Z must be

produced in batches of $7$ moles $(0,7,14,...$ are OK$,$ but not other values that are not multiples of $7).$

Solve the problem using Excel$$s Solver $($or any other solver$).$ Include a clear screenshot of your work,

including the specifications for your solver. Discuss the result in terms of the effect of adding this

constraint.

e$)$ One more constraint: The $$100$ to purchase A and B must be used up$,$ with no money left over.

Solve the problem using Excel$$s Solver $($or any other solver$).$ Include a clear screenshot of your work,

including the specifications for your solver. Discuss the result in terms of the effect of adding this

constraint.