Questions:
- In class we covered two models of population growth: exponential growth and logistic growth. Write a paragraph explaining the advantages and disadvantages of each model, and for each model, give an example of where it may be useful. [6 marks] 2. Consider the following linear programming problem:
a) maximize z = 2×1 + 5×2
subject to
- x2 2xi + x2 < 6 x2 < 5 xi, x2 > 0
(a) Plot the feasible region, and find the optimal feasible solution by investigating comer points. 8 marks Solve the problem using the simplex method (by hand). 8 marks Find the amount which the coefficient in front of xs in the objective function can change without changing the optimal solution. 4 marks Find the amount by which the value on the right hand side of the first constraint can change without making the optimal solution infeasible. [4 marks]
- Consider the following linear programming problem:
a) minimize z = 9×1 + 15×2
subject to xi + 3×2 > 1 2×1 + 2×2 > 9 3×1 + 2×2 > 1 xi, x2 > 0
(a) Formulate the dual problem. 4 marks Solve the dual problem by hand using the simplex method. 8 marks U. matlab to solve the primal problem. Include a copy of your code. [6 marks] - Formulate a linear programming problem with four variables that has an unbounded feasible region but an optimal solution. Demonstrate why your problem has the required properties. [5 marks]
- Consider the following linear programming problem:
a) minimize z = 9×1 + 15×2
subject to xi + 3×2 > 1 2×1 + 2×2 > 9 3×1 + 2×2 > 1 xi, x2 > 0
(a) Formulate the dual problem. 4 marks Solve the dual problem by hand using the simplex method. 8 marks U. matlab to solve the primal problem. Include a copy of your code. [6 marks] - Formulate a linear programming problem with four variables that has an unbounded feasible region but an optimal solution. Demonstrate why your problem has the required properties. [5 marks]
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Sample Solution
