Formulate the following problems as linear optimization models. Where appropriate,

it may be useful to number the commodities and then use subscripted variables.

In some cases no specific objective is named; it is up to the reader to come

up with an appropriate objective.

Each problem could be interpreted as having three parts:

$($a$)$ Define the variables and give the algebraic model.

$($b$)$ Make a model in LINGO or the Excel Solver and find the solution.

$($c$)$ Give a recommendation in words to management.

Check with your professor about what is required for these problems. In addition

to doing all three parts, some alternatives might be to provide the only the algebraic

model, or to omit the algebraic model but with a definition of the variables

included in the LINGO or Excel Solver model.

$1.$ A company blends two gasolines from Avalon Fuels and Bonavista Petrol

$($inputs$)$ into two commercial products, Extra and Regular gasoline $($outputs$).$

For the inputs, the octane ratings, the vapour pressures in kilopascals,

and the amounts available in cubic metres $($m$3)$ and their prices are known.

These are: