A paint produces both interior and exterior paints from two raw materials, $M1$ and $M2.$ The

following table provides the basic data of the problem:

The daily demand for interior paint cannot exceed that for exterior paint by more than $1$ ton.

Also, the maximum daily demand for interior paint is $2$ tons. Your goal is to determine the daily

amounts of exterior and interior paints to be produced for maximum profit. Perform the

following steps:

a$)[5$pt$]$ Formulate a linear programming problem mathematically. Clearly define the

decision variables, objective and constraints.

b$)[5$pt$]$ Solve the problem using Excel's solver. $($i$.$e$.,$ Show that Excel or Python cannot

solve this problem and report a screenshot of the error$).$

c$)[5$pt$]$ Plot the feasible domain to show why Excel or Python cannot solve the problem.

d$)[5$pt$]$ Add a new constraint based on your own judgement to make problem solvable

$($there infinitely any possible ways to do that$),$ and solve it using Excel's solver or

Python's linprog function.