As a part of a quality improvement initiative, employees of mindwork must complete a three day training program a teaming and a two day training program on problem solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem solving be offered during the next six months . In addition ,s senior management has a specific that at least 25 total training program must be offered during this period. The consultant that teaches these training program has 84 available days of training time. MIndwork pays the consultant $2,500 for each program on teaming and $2,000 for each program on problem solving.
Develop a linear programming model that can be used to find the number of each type of training program that should be offered in order to minimize total cost. Solve for the minimal cost solution using the graphical method , and determine the associated costs.