Quain Lawn and Garden, Inc. Case Analysis Essay

by and by a false retirement Bill and Jeanne Quain realized their destined action in the plant and bush business. The need for a high-quality commercial fertilizer prompted the innovation of a blended fertilizer called Quain-Grow. Working with chemists at Rutgers University, a mixture was constructed from quaternity compounds, C-30, C-92, D-21 and E-11.Specifications (i.e constraints) for the mixture demanded that Chemical E-11 must constitute for at least 15% of the blend, C-92 and C-30 must unitedly constitute at least 45% of the blend, and D-21 and C-92 outhouse together constitute no more than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound radixs.The objective of this depth psychology is to determine what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer. To do this we have used unidimensional Programming (LP) a technique specifically designed to attend to managers make decisions relative to the alloc ation 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 constraintthat C-11 must constitute for at least 15% of the blend can be verbalised as . The second constraint that C-92 and C-30 must together constitute at least 45% of the blend can be denotative as . The triad constraint that D-21 and C-92 can together constitute no more than 30% of the blend can be expressed as . Lastly, the fourth 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 calculated and expressed as .These results show that we can recommend the by-line ratios of C-30, C-92, D-21 and E-11 respectively so that the cost of a 50-lb bag of fertilizer is minimized 7.5 lbs, 15 lbs, 0 lbs and 27.5 lbs. In ch ecking to see if these align with the given restraints we found the following to be true and . The actually cost result of this minimization synopsis was calculated to be $3.35 per 50 lb bag of fertilizer. The equation for this result is as follows . Additionally, we performed a aesthesia analysis to project how much our recommendation may change if there are changes in the variables or input entropy. This type of analysis is also called post bestity analysis. There are two approaches to determining just how sensitive an optimal solution is to changes (1) a trial-and-error approach and (2) the analytic postoptimality method. In this case analysis we used the analytic postoptimality method.After we had solved the LP problem, we used the POM software to determine a range of changes in problem parameters that would not bear on the optimal solution or change the variables in the solution. While using the information in the sensitivity report, it is pertinent to assume the conface ration of a change to only a single input data value at a time. This is because the sensitivity information does not generally apply to simultaneous changes in several input data values. Our main objective when performing this analysis was to obtain a empennage price (or dual value) the value of one additional unit of a scarce resource in LP. In any scenario, the shadow price is well-grounded as long as the right-hand side of the constraint stays in a range within which all current corner points move to exist.The information to compute the upper and lower limits of this range is given by the entries labeled Allowable increment and Allowable Decrease in the sensitivity report. Our results from the sensitivity analysis were produced in two parts. The first shows the concussion of changing the objective function coefficients on the optimal solution and gives the range of values (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 Dual Value (Shadow Price), with the lower and upper bounds for which the shadow price is valid.Lastly, these results explain that the price of C-30 can vary within the range of .09 to timelessness without affecting the optimal solution. Likewise the range for C-92 is between Infinity and .12, the range for D-21 is between 15 and 42.5, and the range for E-11 is between 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 between Infinity and 27.5. Constraint 2 has a dual value of -.08 and is valid between 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 between 30 and Infinity.