Decision Support Report - doc

Added on - 28 May 2020

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Running Head: DECISION SUPPORTDecision SupportName of the StudentName of the UniversityAuthor Note
1Table of ContentsYear 2010.........................................................................................................................................3Section A.....................................................................................................................................3Question 2................................................................................................................................3Question 3................................................................................................................................5Section B......................................................................................................................................8Question 4:...............................................................................................................................8Question 5..............................................................................................................................10Question 6..............................................................................................................................11Year 2011.......................................................................................................................................14Section A...................................................................................................................................14Answer 2................................................................................................................................14Section B....................................................................................................................................15Answer 4................................................................................................................................15Answer 5................................................................................................................................16Answer 6................................................................................................................................182012...............................................................................................................................................20Section A...................................................................................................................................20Answer 2................................................................................................................................20Section B:...............................................................................................................................21
2Answer 4:...............................................................................................................................21Answer 5................................................................................................................................22Answer 7................................................................................................................................222013...............................................................................................................................................25Section A...................................................................................................................................25Answer 2................................................................................................................................25Section B....................................................................................................................................25Answer 4................................................................................................................................25Answer 5:...............................................................................................................................26Answer 6:...............................................................................................................................27
3Year 2010Section AQuestion 2Part [a]Here, the objective is to minimize the total cost. Hence, the optimal solution is 740000.The binding constraints;Plant capacity constraintsMarket deviant constraintPart [b]Capacity constraint140000 desks are to be shipped to W/H1 for optimal cost. However, the allowable increase ordecrease in the number of units to be shipped are infinity and 60000 respectively. Thus, if thenumber of desks shipped are more than 80000, there will be no change in the optimal cost.60,000 desks are shipped to W/H2 for optimal cost. However, the allowable increase ordecrease in the number of units to be shipped are 90000 and 10000 respectively. Thus, if thenumber of desks shipped are between 50000 and 150000, the optimal cost will decrease with amultiple of unity.Market demand constraint50,000 desks are received by market 1 for optimal cost. However, the allowableincrease or decrease in the number of units to be received are 90000 and 10000 respectively.Thus, if the number of desks shipped are between 40000 and 140000, the optimal cost willincrease 3 times.
4100,000 desks are received by market 2 for optimal cost. However, theallowable increase or decrease in the number of units to be received are 60000 and 90000respectively. Thus, if the number of desks shipped are between 40000 and 190000, the optimalcost will increase 4 times.50,000 desks are received by market 3 for optimal cost. However, the allowableincrease or decrease in the number of units to be received are 10000 and 50000 respectively.Thus, if the number of desks shipped are between 40000 and 100000, the optimal cost willincrease 4 times.Part [c]This will increase the total cost required to ship the desk from plant 1 to W/H1 hence will notmeet the objective.The new function value will be; = f140000+f120000To warehouse f260000Total cost = 260000+150000+360000+10000+50000= f830000Part [d]When the market 2 demand increases the distribution cost increases because from eitherwarehouse distribution cost is needed. This implies that it has values.This leads to an increase in the optimal solution to take care of the increase in thedistribution cost.Part [e]The shadow price for plant 1 is found to be zero. Thus, there will be no change in cost if theproducts are directly supplied to the markets bypassing the warehouses. Hence, no change ormodification in the distribution plan is required as there will be no impact of this change on theoptimal cost.
5Part [f]Zero reduced cost for shipment between warehouse 1 and market 3 implies that there will beno change in the objective function if the shipment costs are changed.Part [g]Warehouse 2 is currently handling 60,000 desks per. If warehouse 2 cannot handle only 50,000desks per year, this number lies between the allowable limit for the constraint. Thus, theoptimal solution of the LP will increase by its shadow price, that is, the optimal solution willincrease 3 times.Question 3Part [a]Let x1be the number of barrels of pruned olives and x2be the number of barrels of regular olives.Max Z = 20 x1+ 30 x2Subject to the constraints:5 x1+ 2 x2≤ 250x1+ 2 x2≤ 1501.5 x1≤ x2x1, x2≥ 0 and takes only integer values.Part [b]
6Extreme Point Co OrdinatesObjective Function ValueO (0, 0)20 (0) + 30 (0) = 0A (0, 75)20 (0) + 30 (75) = 2250B (25, 62.5)20 (25) + 30 (62.5) = 2375C (31.25, 46.875)20 (31.25) + 30 (46.875) = 2031.25Hence, the optimal solution is given by x1= 25, x2= 62.5 and the maximum profit is£2375Part [c]Putting the values of the optimal x1and x2in the constraint equations,5 (25) + 2 (62.5) = 250, thus, this is a binding constraint(25) + 2 (62.5) = 150, thus this is a binding constraint1.5 (25) ≤ (62.5), thus this is a non-binding constraintNone of the constraints are redundantd)The shadow price for the labour constraint has been determined as 1.25, the shadowprice of the land constraint is 13.75 and the shadow price for the third constraint relating to thenumber of olives is 0.
7e)If the profit of regular olives increases to £45 per barrel, the new optimal profit becomes£3375.Extreme Point Co OrdinatesObjective Function ValueO (0, 0)20 (0) + 45 (0) = 0A (0, 75)20 (0) + 45 (75) = 3375B (25, 62.5)20 (25) + 30 (62.5) = 3312.5C (31.25, 46.875)20 (31.25) + 30 (46.875) =2734.375The maximum value of the objective function z = 3375 occurs at the extreme point (0, 75).Hence, the optimal solution to the given problem is x1 = 0, x2 = 75 and max z = 3375.
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