Given the Following Linear Program:
the Graphical Solution to the Problem

question 34

Essay

Given the following linear program:
The graphical solution to the problem is shown below.From the graph we see that the optimal solution occurs at x₁ = 5,x₂ = 3,and z = 46.
$\mathrm{M} A X \quad 5 X_{1}+7 X_{2}$

s.t
$\begin{aligned} x 1 & \leq 6 \\ 2 x_{1}+3 x_{2} & \leq 19 \\ x_{1}+x_{2} & \leq 8 \\ x_{1}, x_{2} & \geq 0 \end{aligned}$
a.Calculate the range of optimality for each objective function coefficient.
b.Calculate the dual price for each resource.

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Definitions:

Substitution Effect

This refers to the economic theory that as prices rise or fall, consumers will replace more expensive items with less costly alternatives.

Income Effect

Refers to the change in an individual's or economy's income and how that change will affect the quantity demanded of a good or service.

Tax Rate

The rate at which taxes are applied to an individual or a corporation’s income.

Consumption Tax

A tax on the purchase of goods and services, levied at the point of sale.