Shale Oil refinery blends two petroleum stocks, A, and B, to produce two high­ o

Question

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.

Explanation / Answer

A = bbl/hr of Stock A

B = bbl/hr of Stock B

YAi = bbl/hr of A used in gasoline i

YBi = bbl/hr of B used in gasoline i

i = 1, Z

Maximize Z = 7 ( YA1 +  YB1) + 10 ( YAz +  YBz)

s.f.

A = YA1 + YAz , A<=450

B = YB1+  YBz, B<=700

98 YA1 + 89 YB1 >= 91 ( YA1 + YB1)

98 YAZ + 89 YBZ >= 93 ( YAZ + YBZ)

10 YA1 + 8 YB1 >= 12 ( YA1 + YB1)

10 YAZ + 8 YBZ >= 12 ( YAZ + YBZ)

All variables are non negative

Optimum Solution :

Z = $ 10,675

A = 450 bbl/hr

B = 700 bbl/hr

Gasoline 1 production = YA1 + YB1 = 61.11 + 213.89 = 275 bbl/hr

Gasoline 2 production = YAZ + YBZ = 388.89 + 486.11 = 875 bbl/hr

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