1. As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on team building and a two-day training program on problem solving. The manager of quality improvement 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 quarter, 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.

1. 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.
2. Graph the feasible region
3. Determine the coordinates of each extreme point
4. Solve for the minimum-cost solution.

2. Southern oil Company produces two grades of gasoline; regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil. A crude oil and each gallon of premium gasoline contain 0.6 gallons of grade A crude oil. For the next production period Southern Oil has a total of 18,000 gallons of grade A crude oil available. The refinery used to produce the two types of gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

1. Formulate and solve the linear programming model that can be used to determine the number of gallons of regular and premium gasoline that should be produced in order to maximize total profit contributions.
2. What is the optimal solution?
3. What are the values and interpretations of the slack variables?
4. What are the binding constraints?