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:

Input Octane Vapour Amount Buying Price

Gasoline Rating Pressure $($kPa$)$ Available $($m

$3$

$)($$ per m

$3$

$)$

Avalon $993855,000520$

Bonavista $825580,000440$

$204$ CHAPTER $3.$ APPLICATIONS OF LINEAR MODELS

For the Extra and Regular gasolines the requirements are:

Output Minimum Maximum Minimum Selling

Gasoline Octane Vapour Amount Price

Rating Pressure $($kPa$)$ Required $($m

$3$

$)($$ per m

$3$

$)$

Extra $944036,000540$

Regular $865270,000470$

Let the variables be defined as follows: e and r are respectively the amount

of Extra$/$Regular gasoline in m

$3$ blended and sold; a and b are respectively the amount of gasoline in m

$3$ purchased from Avalon Fuels$/$Bonavista

Petrol; ae$,$ ar$,$ be$,$ and br are respectively the amounts in m

$3$ of Avalon$/$Bonavista

gasoline used to make Extra$/$Regular gasoline