Given the Following All-Integer Linear Programming Problem A Solve the Problem Graphically as a Linear Program

question 5

Essay

Given the following all-integer linear programming problem:


$$\begin{array} { l } \operatorname { Max } \quad 3 x _ { 1 } + 10 x _ { 2 } \\\\\text { s.t. } 2 x _ { 1 } + x _ { 2 } \leq 5 \\x _ { 1 } + 6 x _ { 2 } \leq 9 \\\begin{aligned}x _ { 1 } - x _ { 2 } & \geq 2 \\x _ { 1 } , x _ { 2 } & \geq 0 \text { and integer }\end{aligned} \\\end{array}$$
a. Solve the problem graphically as a linear program.
b. Show that there is only one integer point and it is optimal.
c. Suppose the third constraint was changed to x₁ - x₂ > 2.1. What is the new optimal solution to the LP? ILP?

Explain the role of heuristics in influencing human judgment.

Recognize the impact of availability and representativeness heuristics on evaluating information.

Describe the concept of fundamental attribution error and its exceptions.

Identify the consequences of the anchoring and adjustment heuristic in estimation processes.

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Definitions:

Attachment Style

Attachment style pertains to the patterns of expectations, needs, and emotional behaviors that individuals form in close relationships, rooted in early interactions with caregivers.

Infant Attachment Styles

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Self-fulfilling

A prediction or expectation that causes itself to become true by the very terms set forth or by the behaviors it induces.

Evolutionary Theory

A scientific explanation of the origins of species of plants and animals, emphasizing natural selection and genetic variation.