Given the Following Linear Program The Graphical Solution to the Problem Is Shown Below

question 60

Essay

Given the following linear program:
$$\begin{array} { l r } \operatorname { Max } & 5 x _ { 1 } + 7 x _ { 2 } \\\text { s.t. }& x _ { 1 } \leq 6 \\ & 2 x _ { 1 } + 3 x _ { 2 } \leq 19 \\& x _ { 1 } + x _ { 2 } \leq 8 \\& x _ { 1 } , x _ { 2 } \geq 0\end{array}$$
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 obj.func.= 46.
a.Calculate the range of optimality for each objective function coefficient.
b.Calculate the dual price for each resource.

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Definitions:

Required Return

The minimum gain or profit that an investor expects to earn from an investment, considering the level of risk involved.

Capital Gains Yield

The price appreciation component of the total return on an investment, excluding dividends if any.

Dividend Yield

An indicator of the proportion of dividends disbursed annually by a company to the price of its shares.

Preemptive Rights

Rights that allow existing shareholders to purchase additional shares before the company offers them to the public, helping to maintain their ownership percentage.