As a part of quality improvement initiative, IBM employees complete a three-day training program on teaming and two- day training program on problem solving. The manager of quality improvement has requested at least eight training programs on teaming and at least ten training programs on problem solving be offered during the next six months. In addition, senior –level management has specified that at least 25 training programs must be offered during this period. IBM uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training available. Each training program on teaming costs $10,000 and each training program on problem solving costs $8,000.

a) Develop a mathematical linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem solving that should be offered in order to minimize the cost. (Identify decision variable(s), objective function, and constraints)

b) Graph the feasible solution.

c) Determine the coordinates of each corner point.

d) Solve for the minimum cost (Optimal Solution).