3. What is the objective function value for the objective function line through the point (3,5)? (Another name for the objective function line is isoprofit line, see page 24 in the textbook for a description.)
4. What is the objective function value for the objective function line through the point (4,4)? Is this an improvement to the answer in part c?
5. Which best describes the linear program (LP): infeasible, unique optimal solution, alternate optimal solution, or unbounded optimal solution?
6. Consider the following new constraint: The water filtering had to be replaced. The new system will only be able to provide water to a maximum of 7.5 acres of tomatoes. Pepper production is not affected.

• Will the feasible region stay the same, increase, or decrease?
• Will the optimal value stay the same, increase, or decrease?
• If the new constraint does cause the optimal solution and optimal value to change, what are the new optimal solution and optimal value?

3. The formulation of the Organic Greenhouses problem and its graph is shown. Let P be the number of acres of peppers planted. Let T be the number of acres of tomatoes planted. Max: 30,000P+ 40,000T st. 1P + 1T 0 Non-negativity P. T P> 0 (Non-givity) (4,8) Acme of Tommtors 12 11 10(0,10) P8 Max Pepper) 9 8 7 6 (6,6) 15P+ 3T30 (Labor 5 3 2 +10=12 (Land) T> 0 [Nan-negativity 969 (6.0) 1 2 3 10 11 12 13 14 15 16 17 18 19 20 21 4 0 7 Acres of Peppers a. What is the value of the objective function for each of the extreme points? (0,0) (0,10) (4,8) (6,6) (6,0) b. What is the optimal solution