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?

c. What is the objective function value for the objective function line through the point (1,3)? (Another name for the objective function line is isoprofit line, see page 24 in the textbook for a description.)

d. What is the objective function value for the objective function line through the point (2,5)? Is this an improvement to the answer in part c?

e. Which best describes the linear program (LP): infeasible, unique optimal solution, alternate optimal solution, or unbounded optimal solution? Why?

f. Consider the following change to a constraint: Due to hotter than normal temperatures, two acres of land have been deemed unusable for these crops.

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

Please help, thank you!

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+40,000Tst.1P+1T12Land1.5P+3T30Labor1P6MaxAcresofPepperP,T0Non-negativity