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Warning: TT: undefined function: 32 Warning: TT: undefined function: 32 Define 12 variables such that: AA: Barrels of region A oil used in type A. .. BD: Barrels of region B oil used in type D. Then, you must have 15 constraints: 3 available amount from regions, 4 demand constraints and 4 each for m...

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1. Define 12 variables such that: AA: Barrels of region A oil used in type A. .. BD: Barrels of region B oil used in type D. Then, you must have 15 constraints: 3 available amount from regions, 4 demand constraints and 4 each for minimum and maximum ratios of type A and C. Min 10*( AA+AB+AC+AD)+20*( BA+BB+BC+BD)+30*( CA+CB+CC+CD) AA+AB+AC+AD =250 AD+BD+CD>=250 AA=0.3*( AD+BD+CD) AA, AB,AC,AD,BA,BB,BC,BD,CA,CB,CC,CD >= 0 (nonnegativity) 2. 3. Apply formulas, straightforward. 4. Apply formulas, for significance just look at the significance of F and p-values. 5. In this question my intention was designed by mistakenly seeing allowed increase in demand of D constraint as 14 instead of -5… E-14. Notice E-14 means 10^(-14) which is practically 0, in that case we can’t decide on what would happen with the changes in a and b by sensitivity report, because an increase by 10 is beyond allowed increase limit. If it was 14 instead, a.) 10/14 is less than 1 so we can check, shadow price is 0 so cost would stay same. b.) Demand of D increase by 10 units, demand of A decrease by 10 units. Comparing these with their corresponding allowed increase and decrease, and checking 100% rule: 10/14+10/83.3333 < 1 so we can make calculations based on shadow prices. Then, change in cost is 10*0+(-10)*0.3=-3 dollars, so our cost decrease.(Notice, change in A is -10). c.) A decrease by 50 units, 50/83.333120. This student missed the office hour. Therefore, if the index(order, student count, id etc.) of this student is N, number of students served is N-1. Replicate large number of times. Take the average of number of students served....