Shale Oil refinery blends two petroleum stocks A and B to pr

Shale Oil refinery blends two petroleum stocks, A, and B, to produce two high­ octane gasoline products, I and II. Stocks A and B are produced at the maximum rates of 450 and 700 bbl/hr, respectively. The corresponding octane numbers are 98 and 89, and the vapor pressures are 10 and 8lb/in2 • Gasoline I and Gasoline II must have octane numbers of at least 91 and 93 respectively. The vapor pressure associated with both (each) products should not exceed 12lb/in2• Octane number and vapor pressure of the Gasoline I and II are calculated as weighted averages of blended stocks. The profits per bbl of I and II are $7 and $10, respectively

. a. Develop an LP model (a tableau) to determine the optimum production rate for I and II and their blend ratios from stocks A and B.

b. Solve using excel solver. Report the solutions table generated by the solver.

Solution

A = bbl/hr of Stock A

B = bbl/hr of Stock B

Y_Ai = bbl/hr of A used in gasoline i

Y_Bi = bbl/hr of B used in gasoline i

i = 1, Z

Maximize Z = 7 ( Y_A1 +  Y_B1) + 10 ( Y_Az +  Y_Bz)

s.f.

A = Y_A1 + Y_{Az ,} A<=450

B = Y_B1+  Y_Bz, B<=700

98 YA1 + 89 Y_B1 >= 91 ( Y_A1 + Y_B1)

98 Y_AZ + 89 Y_BZ >= 93 ( Y_AZ + Y_BZ)

10 Y_A1 + 8 Y_B1 >= 12 ( Y_A1 + Y_B1)

10 Y_AZ + 8 Y_BZ >= 12 ( Y_AZ + Y_BZ)

All variables are non negative

Optimum Solution :

Z = $ 10,675

A = 450 bbl/hr

B = 700 bbl/hr

Gasoline 1 production = Y_A1 + Y_B1 = 61.11 + 213.89 = 275 bbl/hr

Gasoline 2 production = Y_AZ + Y_BZ = 388.89 + 486.11 = 875 bbl/hr