Please help me with this. I\'m getting myself very confused. I need an explanati

Question

Please help me with this. I'm getting myself very confused. I need an explanation.

An oil company produces three brands of oils: Regular, Multigrade, and Supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different viscosity index. The relevant data concerning the crude stocks are: Each brand of oil must meet a minimum standard for viscosity index, and each brand thus sells at a different price. The relevant data concerning the three brands of oil are: Completely formulate this problem as an optimal production plan for a single day, assuming all oil produced during this day can be either sold or stored at negligible cost Do not solve this problem.

Explanation / Answer

one of the 3 scenarios can occur

low demand probablity=0.2

medium demand probablity=0.5

high demand prbablity =0.3

var s1>0,s2>0,s3>0,s4>0

m1>0,m2>0,,m3>0,m4>0

r1>0,r2>0,r3>0,r4>0

max profit= (10*(s1+s2+s3+s4) +(9*(m1+m2+m3+m4)+ (8.5*(r1+r2+r3+r4)+(7.7*(s3+m3+r3)+(9*(s4+m4+r4))

con crude1 supply : s1+r1+m1<=2000

con crude2 supply : s2+m2+r2<=1100

con crude3 suppy :s3+m3+r3<=1200

con crude4 supply: s4+m4+r4<=1100

con supreme demand : s1+s2+s3+s4<=750

con multigarde demand : m1+m2+m3+m4<=4500

con regulardemand : r1+r2+r3+r4<=2000

con_vsupreme :(1/(s1+s2+s3*s4))*(20*s1+40*s2+30*s3+55*s4)>=50

con_vmultgrad :(1/(m1+m2+m3+m4))*(20*m1+40*m2+30*m3+55*m4)>=35

con_vregular : (1/(r1+r2+r3+r4))*(20*r1+40*r2+30*r3+55*r4)>=25

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