The Better Lawn Company manufactures two types of lawn trimmers: an electric model and a gas model. The company has contracted to supply a national discount retail chain with a total of 30,000 electric trimmers and 15,000 gas trimmers. However, Better Lawn’s’s production capability is limited in three departments: production, assembly, and packaging. The following table summarizes the hours of processing time available and the processing time required by each department, for both types of trimmers.
Electric Gas Hours Available
Production 0.2 0.4 10,000
Assembly 0.3 0.5 15,000
Packagin 0.1 0.1 5,000
The company makes its electric trimmer in-house for $55 and its gas trimmer for $85. Alternatively, it can buy electric and gas trimmers from another source for $67 and $95 respectively. How many gas and electric trimmers should Better Lawn make and how many should it buy from its competitors in order to fulfill its contract in the least costly manner?
Part a) For the application described above, develop a complete LP model below, with decision variables, objective function and constraints.
Part b) Proceed to create a spreadsheet model
Part c) Solve the LP for the optimal solution