Golding Landscaping
Golding Landscaping and Plants
Cynthia (Matson) Kain
Daniel Webster College
Nashua, New Hampshire
6-23-2013
THE PROBLEM
To formulate a problem in linear programming, there are three steps in the process; decision variables, an objective function and constraints.
Decision variables or “unknown entities” tell us what we are solving for (Balakrishnan, 2013). In the Golding Landscape case, we are solving for variables to tell us which combination of chemicals will produce the most cost effective results given the constraints.
The objective function is to combine these chemicals in such a way as to create a blend of fertilizer that will optimally suit the northern Virginia climate at the most minimized cost.
The constraints are the specifications set forth by the chemists at George Mason University.
CHART
| C-30 | C-92 | D-21 | E-11 | | | | # of pounds | 7.50 | 15.00 | 0.00 | 27.50 | | | | Cost | $0.12 | $0.09 | $0.11 | $0.04 | $3.35 | | | Constraints | | | | | | | | 50-lbs required | 1 | 1 | 1 | 1 | 50.00 | = | 50.0 | E-11 >= 15% | | | | 1 | 27.50 | >= | 7.5 | C-92 & C-30 >= 45% | 1 | 1 | | | 22.50 | >= | 22.5 | D-21 & C-92 <= 30% | | 1 | 1 | | 15.00 | <= | 15.0 | | | | | | LHS | Sign | RHS |
In the chart above, the decision variables are highlighted in yellow. The objective function is green and the blue denotes the left hand side of the constraints formula (Balakrishnan, Managerial Decision Modeling Companion Website, 2012).
GRAPHICAL SOLUTION
When plotting the chart figures (above) on a graph (below), the following is exhibited.
Determining the feasible solution region (where all of the problem constraints overlap) is the goal.
CONCLUSION/RISKS
At this juncture, without the ability to access excel solver, drawing conclusions about the data and the risks associated with this case study is limited to my basic knowledge. That said, it appears that when
Cynthia (Matson) Kain
Daniel Webster College
Nashua, New Hampshire
6-23-2013
THE PROBLEM
To formulate a problem in linear programming, there are three steps in the process; decision variables, an objective function and constraints.
Decision variables or “unknown entities” tell us what we are solving for (Balakrishnan, 2013). In the Golding Landscape case, we are solving for variables to tell us which combination of chemicals will produce the most cost effective results given the constraints.
The objective function is to combine these chemicals in such a way as to create a blend of fertilizer that will optimally suit the northern Virginia climate at the most minimized cost.
The constraints are the specifications set forth by the chemists at George Mason University.
CHART
| C-30 | C-92 | D-21 | E-11 | | | | # of pounds | 7.50 | 15.00 | 0.00 | 27.50 | | | | Cost | $0.12 | $0.09 | $0.11 | $0.04 | $3.35 | | | Constraints | | | | | | | | 50-lbs required | 1 | 1 | 1 | 1 | 50.00 | = | 50.0 | E-11 >= 15% | | | | 1 | 27.50 | >= | 7.5 | C-92 & C-30 >= 45% | 1 | 1 | | | 22.50 | >= | 22.5 | D-21 & C-92 <= 30% | | 1 | 1 | | 15.00 | <= | 15.0 | | | | | | LHS | Sign | RHS |
In the chart above, the decision variables are highlighted in yellow. The objective function is green and the blue denotes the left hand side of the constraints formula (Balakrishnan, Managerial Decision Modeling Companion Website, 2012).
GRAPHICAL SOLUTION
When plotting the chart figures (above) on a graph (below), the following is exhibited.
Determining the feasible solution region (where all of the problem constraints overlap) is the goal.
CONCLUSION/RISKS
At this juncture, without the ability to access excel solver, drawing conclusions about the data and the risks associated with this case study is limited to my basic knowledge. That said, it appears that when
Bibliography: Balakrishnan, N. (2012). Managerial Decision Modeling Companion Website. Retrieved from Pearson Education: http://wps.prenhall.com/bp_balakrishnan_mdms_3/219/56162/14377680.cw/index.html Balakrishnan, N. (2013). Managerial Decision Modeling with Spreadsheets. Upper Saddle River, NJ: Pearson. Rowles, K. (2000, September 1). Market Research for New Products. Retrieved from Cornell.edu: http://hortmgt.dyson.cornell.edu/pdf/smart_marketing/rowles9-00.pdf