The Optimal Solution of the Linear Programming Problem Is at the Intersection

question 63

Essay

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.
$$\begin{array} { l l } \operatorname { Max } & 2 x _ { 1 } + x _ { 2 } \\\text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \\& 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \\& 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \\& x _ { 1 } , x _ { 2 } \geq 0\end{array}$$
a.Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.

Comprehend the genetic basis and conservation of circadian rhythms across species.

Recognize key historical figures in animal behavior and their contributions.

Analyze circadian rhythms in experimental settings.

Interpret animal communication methods, such as the honey bee waggle dance.

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Definitions:

Liberia

A country on the West African coast founded by freed American and Caribbean slaves as a colony for African American resettlement.

Haiti

A country on the island of Hispaniola in the Caribbean, notable for being the first black-led republic and the first independent Caribbean state after its revolt against French colonial rule.

Lynch Mob

A group of people who, without legal authority, come together to execute a presumed offender, often by hanging, primarily targeting African Americans.

Springfield, Ohio

A city in the United States known for its historical contributions to industry, education, and the antislavery movement.