Consider the Following Linear Program

question 2

Essay

Consider the following linear program:
Max
60X + 43Y
s.t.
X + 3Y ≥ 9
6X − 2Y = 12
X + 2Y ≤ 10
X, Y ≥ 0
​
a.
Write the problem in standard form.
b.
What is the feasible region for the problem?
c.
Show that regardless of the values of the actual objective function coefficients, the optimal solution will occur at one of two points. Solve for these points and then determine which one maximizes the current objective function.

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Definitions:

Transfer

The movement of something from one place, person, or ownership to another, often without the exchange of money.

Regressive Tax Structure

A tax system where the rate decreases as the taxable amount increases, disproportionately affecting lower-income individuals.

Proportion

A part, share, or number considered in comparative relation to a whole.

Income

The money received by an individual or group for their labor, investments, or other revenue-generating activities.