Production Planning Problem #$3$

Recall the third problem statement for lab $2.$

Parameters

Maximum number of oil barrels: $20(1000$ barrels$)$

Time to process $1000$ barrels: $1$ hour $($aviation oil$),45$ minutes $($heating oil$)$

Available time: $8$ hours

Revenues per $1000$ barrels: $$60($aviation fuel with no further processing$),$ $$40($heating oil with no further processing$),$ $$130($aviation fuel with further processing$),$ $$90($heating oil with further processing$)$

Cost per $1000$ barrels: $$40$

Decision Variables

$y$ : number of $1000$ barrels purchased

$x_1$ : number of $1000$ barrels of aviation oil distilled

$x_2$ : number of $1000$ barrels of heating oil distilled

$x_3$ : number of $1000$ barrels of aviation oil distilled with further processing

$x_4$ : number of $1000$ barrels of heating oil distilled with further processing

Constraints

$y20($total amount of barrels sold should not exceed the maximum number of barrels that can be purchased$)$

$x_3+0\mathrm{.}75x_{4}8($total amount of processing time should not exceed the total available time$)$

$x_3{x}_1($total of processed aviation oil should not exceed the total amount of distilled aviation oil$)$

$x_4{x}_2($total of processed heating oil should not exceed the total amount of distilled heating oil$)$

$x_1=0\mathrm{.}5y($total amount of non$-$processed aviation oil is equal to half the total amount of oil purchased$)$

$x_2=0\mathrm{.}5y($total amount of non$-$processed heating oil is equal to half the total amount of oil $.$ purchased$)$

$x_1,x_2,x_3,x_4,y0($variable restrictions$)$

Objective function

Maximize $-40y+60(x_1-x_3)+40(x_2-x_4)+130x_3+90x_4$