I DO NOT NEED THE LINEAR PROGRAMMING MODEL (a) - ONLY THE CONSTRAINTS!

As a part of quality improvement initiative, United Technologies employees must complete a fourday training program on team building and a three-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. United Technologies 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 $8,000 and each training program on problem solving costs $6,000. (a) Formulate a linear programming model that can be used to determine the number of training programs on team building and the number of training programs on problem solving that should be offered in order to minimize total cost. In 12A(a), suppose the following changes are made. 1. United Technologies (UT) must offer 3-day training program on time management, at a cost of $5,000 each, in addition to the two programs mentioned in the problem. 2. It must offer at least 16 of the time management programs during the next 6 months. 3. With the addition of the time management training program, the total number of training programs must now be at least 30 (instead of 25 ). 4. Fortunately, UT was able to hire one additional consultant who has 84 days available, effectively doubling the total available training time. Write down only the 2 new constraint expressing \#3 about the total number of training programs and \#4 about the total available training time. Do not write any other constraints here. 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