A company wants to offer their employees a three-day training program on team building and a two-day program on problem solving. They have requested at least 8 training sessions on team building and at least 10 training sessions on problem solving. Furthermore, the total number of training sessions offered must be 25.

The training consultant has 84 days of training time available.

Each training session on team building costs $10,000 and each training session on problem solving costs $8,000.

Formulate a Linear Programming Model that can be used to determine the number of training sessions on team building and the number of training sessions on problem solving that should be offered in order to minimize total cost.

Identify the varibles, formulate the objective function, determine all the constraints as linear inequalities, clearly identify the critical region, solve the coordinates of the corner points of the critical region and identify which corner points minimize the objective function.