LINEAR PROGRAMMING

DEVELOPING LINEAR PROGRAMMING MODELS

Example $4\mathrm{.}5$

A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three $(3)$ processors: a cracker, a splitter and a separator. To produce one barrel of Super requires $3$ hours for cracker, $2$ hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires $4$ hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most $66$ hours for cracker, $180$ hours for splitter and $200$ labour hours for separator. In addition, it cost the producer $GH45\mathrm{.}00$ and $GH90\mathrm{.}00$ per barrel to produce Super and Diesel respectively. Selling prices per barrel of Super and Diesel are $GH135\mathrm{.}00$ and $GH165\mathrm{.}00$ respectively.

IUPSA

Service Excellence

$16$

LINEAR PROGRAMMING

DEVELOPING LINEAR PROGRAMMING MODELS

$($a$)$ Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation$.$

$($b$)$ Determine how many barrels of each item should be produced to maximize profit;

$($c$)$ Determine the scarce resources

$($d$)$ Find the shadow prices of the resources available to the firm.

$($e$)$ If there is an hour increase each in the scarce resources what will be the effect on profit?

$($f$)$ What output should be produced if profit on diesel increase by $GH20$ per barrel.