Due: $30/10/2024$ at $03$:$30$ p$.$m$.$

Problem $5(25)$

Alkylate, cat cracked gasoline, and straight run gasoline are blended to make aviation gasolines A and B and two grades of motor gasoline. The specifications on motor gasoline are not as rigid as for aviation gas. Physical property and production data for the inlet streams are as follows:

$\backslash$table$[[$Stream$,$RVP$,$ON$(0),$ON$(4),\backslash$table$[[$Available$],[($bbl$/$day$)]]],[$Alkylate$,5,94,108,4000],[$Cat cracked gasoline,$8,84,94,2500],[$Straight run gasoline,$4,74,86,4000]]$

Abbreviations:

RVP: Reid vapor pressure $($measure of volatility$)$

ON: octane number; in parentheses, number of $m\frac{l}{g}al$ of tetraethyl lead $($TEL$).$

For the blended products:

$\backslash$table$[[$Product$,$TEL,$],[$RVP$,$Level,ON$,$Profit $($$$/$bbl$),],[$Aviation gasoline A$,7,0,80,5\mathrm{.}00],[$Aviation gasoline B$,7,4,91,5\mathrm{.}50],[$Leaded motor gasoline,$-,4,87,4\mathrm{.}50],[$Unleaded motor gasoline,$-,0,91,4\mathrm{.}50]]$

i$-,$ Set up this problem as a "Linear Program" and solve it using the Excel Solver.

ii$-,$ By looking at the sensitivity report, would you try to increase the availability of Alkylate, Cat cracked gasoline or Straight run gasoline? Justify. If you can buy it in the market, how much would you pay for it$?$

Note: Assume that the properties $($i$.$e$.$ RVP and ON$)$ blend linearly. Namely, if two : and F$2$ and properties P$1$ and P$2$ mix, the property P$3$ of the resulting blend satisfic

$\frac{3}{4}$

To

relationship, $F{1}^{**}P1+F{2}^{**}P2=(F1+F2{)}^{**}$ P$3.$

Hint: Pay particular attention on how to formulate the problem to be linear. Intuitively you may try to model it as a nonlinear program.