As a part of quality improvement initiative, Consolidated Electronics employees do a three-day training program on team building and a two-day training program on problem solving.The manager has requested that at least 8 training programs on team building and at least 10 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.Consolidated Electronics uses a consultant to teach the training programs.During the next 6 months, the consultant has 84 days of training time available.Each training program on team building costs $10,000 and each training program on problem solving costs $8,000.

In 12-A(a), suppose the following changes are made.Consolidated Electronics must offer 4-day training program on time management in addition to the two programs mentioned in the problem.It must offer at least 6 of the time management programs during the next 6 months.Fortunately, CE was able to hire one additional consultant who has 84 days available, effectively doubling the total available training time.

Write down the new constraint that expresses the limit on total number of days for training programs ("days available" constraint).Use the variables:

T = number of training programs on teaming

P = number of training programs on problem solving

M = number of training programs on time management