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Homework answers / question archive / IEEN 5335-Principals of Optimization 1
IEEN 5335-Principals of Optimization
1. Consider the following linear program and solve questions, 2. a) – 2. c). Max x1 + x2 s.t. x1 + x2 = 3 x1 >= 0 and x2 is free 1. a) Graph the feasible set. Caution: x2 is free.
1. b) Find all corner point feasible solutions (CFS).
1. c) What is the optimal solution
2. Consider the following linear program and its LINDO output. The variables x, y and z are product types, and the objective is to maximize the profit.
Max 2x + 3y + 5z s.t. Material)2x + 7y + 5z <= 20 Labor)3x + 2y + 5z <= 35 x, y, z ≥ 0 --------------------- LINDO output -----------------------
OBJECTIVE FUNCTION VALUE 1) 20.00000
VARIABLE VALUE REDUCED COST X 10.000000 0.000000 Y 0.000000 4.000000 Z 0.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES MATERIAL) 0.000000 1.000000 LABOR) 5.000000 0.000000 NO. ITERATIONS= 4
RANGES IN WHICH THE BASIS IS UNCHANGED:
ARIABLE CURRENT ALLOWABLE ALLOWABLE
E CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X 2.000000 INFINITY 0.000000 Y 3.000000 4.000000 INFINITY Z 5.000000 0.000000 INFINITY RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE MATERIAL 20.000000 3.333333 20.000000 LABOR 35.000000 INFINITY 5.000000 --------------------- LINDO output end -----------------------
Answer the following questions (2. a, b and c) with above LINDO output.
2. a) What is the optimal solution for this problem? How many of each product should be produced to get the optimal solution?
2. b) This problem has multiple optimal solutions, which mean that another combination of products manufacturing can also be the optimal solution. How do you identify if this problem has multiple optimal solutions? You don’t need to find another optimal, but describe how you identify it
2. c) Currently, the coefficient of y is 3 in the objective function. Assume that this value is changed to 2, which makes new objective function, Max 2x + 2y + 5z. Now, somebody said as following: “The new objective value will be bigger than the current value, 20” Is this statement TRUE or FALSE? Why?
3. Build a LP model for the following scenario, but don’t solve the LP model that you made. I just need your model.
There is a company to make mixed juice products. The company wants to maintain the taste of juice by adding and mixing juices, such as orange, banana and pineapple. The sugar content of three juices – orange, banana, and pineapple – is 15, 18, and 25 percent per gallon, respectively. The cost per gallon is $0.80 for orange juice, $1.20 for banana juice, and $1.60 for pineapple juice. How much of each must be mixed together to achieve one gallon of mixed juice that has a sugar content of at least 19 percent to minimize cost?
For full credit, first of all, define the decision variables, and then write objective function and the constraints.
