The Binding Constraints for This Problem Are the First and Second

question 44

Essay

The binding constraints for this problem are the first and second.
Min $\mathrm { x } _ { 1 } + 2 \mathrm { x } 2$
s.t.
$x _ { 1 } + x _ { 2 } \geq 300$
$2 \mathrm { x } _ { 1 } + \mathrm { x } _ { 2 } \geq 400$
$2 \mathrm { x } 1 + 5 \mathrm { x } _ { 2 } \leq 750$
$\mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } \geq 0$
a.Keeping c₂ fixed at 2,over what range can c₁ vary before there is a change in the optimal solution point?
b.Keeping c₁ fixed at 1,over what range can c₂ vary before there is a change in the optimal solution point?
c.If the objective function becomes Min 1.5x₁ + 2x₂,what will be the optimal values of x₁,x₂,and the objective function?
d.If the objective function becomes Min 7x₁ + 6x₂,what constraints will be binding?
e.Find the dual price for each constraint in the original problem.

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Definitions:

Flexible Interest Rate

refers to an interest rate that can change over the term of a loan or deposit based on market conditions.

Credit Supplied

The total amount of credit available to borrowers from lenders within the market.

Aggregate Demand Curve

A graphical representation that shows the total amount of goods and services demanded at different price levels in an economy.

Equilibrium Real GDP

The level of Gross Domestic Product at which aggregate supply equals aggregate demand, resulting in no unintended inventory build-up or depletion.