'Quain Lawn and Garden, Inc. Case Analysis Essay\r'

'After a false retirement Bill and Jeanne Quain established their destined action in the ground and shrub business. The need for a high-quality mer laughingstocktile fertiliser prompted the innovation of a mix fertilizer c exclusivelyed â€Å"Quain-Grow”. Working with chemists at Rutgers University, a mixture was constructed from four compounds, C-30, C-92, D-21 and E-11.\r\nSpecifications (i.e modestys) for the mixture demanded that chemic E-11 essential construct for at least 15% of the intermix, C-92 and C-30 mustiness together constitute at least 45% of the blend, and D-21 and C-92 female genital organ together constitute no more than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound bags.\r\nThe aim of this psychoanalysis is to determine what blend of the four chemicals will allow Quain to minify the cost of a 50-lb bag of the fertilizer. To do this we have apply Linear computer programing (LP) †a technique specifically knowing t o help managers make decisions relative to the apportionment of resources. In this case, C-30 = , C-92 = , D-21 = , and E-11 = . The constraints for this case were translated into linear equations (i.e. inequalities) to mathematically express their meaning. The first constraint that C-11 must constitute for at least 15% of the blend jakes be evince as: . The spot constraint that C-92 and C-30 must together constitute at least 45% of the blend can be expressed as: . The third constraint that D-21 and C-92 can together constitute no more than 30% of the blend can be expressed as: . Lastly, the quarter constraint is that Quain-Grow is packaged and sold in 50-lb bags can be expressed as: . These equations were obtained and entered into a POM LP as a minimizing function. The objective function of this case was compute and expressed as .\r\nThese results show that we can recommend the following ratios of C-30, C-92, D-21 and E-11 respectively so that the cost of a 50-lb bag of ferti lizer is minimized: 7.5 lbs, 15 lbs, 0 lbs and 27.5 lbs. In checking to see if these align with the given restraints we frame the following to be true; ; ; and . The very cost result of this minimization analysis was calculated to be $3.35 per 50 lb bag of fertilizer. The equation for this result is as follows: . Additionally, we performed a sensitivity analysis to abide how much our recommendation may transmute if there ar flip-flops in the variables or stimulus data. This type of analysis is similarly called post bestity analysis. There are two approaches to ascertain just how sensitive an optimal radical is to changes: (1) a trial-and-error approach and (2) the uninflected postoptimality method. In this case analysis we use the analytic postoptimality method.\r\nAfter we had solved the LP problem, we used the POM software to determine a flap of changes in problem parameters that would not affect the optimal solution or change the variables in the solution. While util ize the schooling in the sensitivity report, it is tending(p) to assume the consideration of a change to only a single input data repute at a time. This is because the sensitivity information does not generally apply to simultaneous changes in some(prenominal) input data values. Our main objective when performing this analysis was to obtain a shadow determine (or ternary value) †the value of one additional unit of a scarce resource in LP. In any scenario, the shadow price is effectual as long as the right side of the constraint stays in a flap within which all current corner points continue to exist.\r\nThe information to compute the f number and lower limits of this honk is given by the entries labeled deductible Increase and Allowable Decrease in the sensitivity report. Our results from the sensitivity analysis were produced in two parts. The first shows the impact of changing the objective function coefficients on the optimal solution and gives the range of va lues (lower and upper bound) for which the optimal solution remains unchanged. The second part of the report shows the impact of changing the R.H.S of the constraints of the objective function value, with the help of multiple Value (Shadow Price), with the lower and upper leap for which the shadow price is valid.\r\nLastly, these results explain that the price of C-30 can vary within the range of .09 to Infinity without affecting the optimal solution. overly the range for C-92 is among â€Infinity and .12, the range for D-21 is among 15 and 42.5, and the range for E-11 is amongst 30 and Infinity. The second part of this sensitivity analysis show the ranges for which the shadow prices are valid. Constraint 1 has a dual value of 0 and is valid amidst â€Infinity and 27.5. Constraint 2 has a dual value of -.08 and is valid amongst 15 and 42.5. Constraint 3 has a dual value of .03 and is valid between 0 and 22.5. Finally, Constraint 4 has a dual value of -.04 and is valid be tween 30 and Infinity.\r\n'