Quain Lawn and Garden, Inc. Case Analysis Essay

After a false retirement Bill and Jeanne Quain realized their bound(p) action in the plant and shrub business. The need for a high-quality commercial-grade fertilizer prompted the innovation of a blended fertilizer called Quain-Grow. Working with chemists at Rutgers University, a mixture was constructed from four compounds, C-30, C-92, D-21 and E-11.Specifications (i.e shynesss) for the mixture demanded that Chemical E-11 must crap for at least 15% of the blend, C-92 and C-30 must unneurotic name at least 45% of the blend, and D-21 and C-92 stinker together constitute no more(prenominal) than 30% of the blend. Lastly, Quain-Grow is packaged and sold in 50-pound bags.The objective of this analysis is to feel 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 Linear Programming (LP) a technique specifically designed to help managers make decisions relative to the parceling of resources. In this ca rapace, 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 feces be explicit as . The second 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 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 constitute 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 fertilizer is minimized 7.5 lbs, 15 lbs, 0 lbs and 27.5 lbs. In checking to empathis e if these align with the given restraints we found the following to be true and . The in reality 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 predisposition analysis to project how much our recommendation may change if at that place are changes in the variables or input info. This type of analysis is in like manner called postoptimumity 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 trim of changes in problem parameters that would non affect the optimal solution or change the variables in the solution. while using the information in the predisposition report, it is pertinent to assume the experimental condition of a change to only a single input data value at a time. This is because the sensitivity information does not primarily apply to simultaneous changes in several input data values. Our master(prenominal) objective when performing this analysis was to obtain a shadow expense (or dual value) the value of one additional unit of a simply resource in LP. In any scenario, the shadow price is sound as long as the right-hand side of the constraint girdle in a range within which all current turning point points continue to exist.The information to compute the upper and lower limits of this range is given by the entries labeled Allowable Increase and Allowable Decrease in the sensitivity report. Our results from the sensitivity analysis were produced in two scatters. The first shows the squeeze 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 r emains 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 doubled Value (Shadow Price), with the lower and upper bounds for which the shadow price is effectual.Lastly, these results develop that the price of C-30 can vary within the range of .09 to Infinity without bear on the optimal solution. Likewise the range for C-92 is amid Infinity and .12, the range for D-21 is in the midst of 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. restraint 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.