A refinery manufactures two grades of fuel F1 and F2 by blen

A refinery manufactures two grades of fuel, F1 and F2, by blending four types gasoline, A, B, C, D. Fuel F1 uses gasolines A, B, C, and Din the ratio 1:1:2:4, uel F2 uses the ratio 2:2:1:3. The supply limits for A, B, C, and Dare 1000, 120 00, and 1500 bbl/day respectively. The costs per bbl for gasolines A, B, C, an , are $120, $90, $100, and $150, respectively. Fuels F1 and F2 sell for $200 an 250 per bbl, respectively. The minimum demand for F1 and F2 is 200 and 400 bl/day, respectively. Develop an LP model and determine the optimal roduction mix for F1 and F2.

Solution

F1 F2

A x 2y <=1000

B x 2y <=1000

C 2x y <=1200

D 4x 3y <=1500

>=200 >=400

Maximize 200x + 250y

Constraints:

x>=25

y>=50

x+2y<=1000

2x+y<=1200

4x+3y<=1500

Intersection of x=25 and x+2y=1000, (25,487.5)

Intersection of y=50 and x+2y=1000, (900,50)

Intersection of x=25 and 2x+y=1200, (25,1150)

Intersetion of y=50 and 2x+y=1200, (575,50)