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Problem 10

$\begin{array}{ll}\text { Maximize } & z=3 x_{1}+4 x_{2}+6 x_{3} \\ \text { subject to } & 5 x_{1}-x_{2}+x_{3} \leq 1,500 \\ & 2 x_{1}+2 x_{2}+x_{3} \leq 2,500 \\ & 4 x_{1}+2 x_{2}+x_{3} \leq 2,000 \\ & x_{1} \geq 0, x_{2} \geq 0, x_{3} \geq 0\end{array}$

Expert verified

The optimal solution for the given linear programming problem is \(x_1 = 0\), \(x_2 = 0\), \(x_3 = 1500\), with a maximum value for \(z\) of 9000.

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Chapter 5

Consider the following linear programming problem: $$ \begin{array}{ll} \text { Maximize } & p=x+y \\ \text { subject to } & x-2 y \geq 0 \\ & 2 x+y \leq 10 \\ & x \geq 0, y \geq 0 \end{array} $$ This problem (A) must be solved using the techniques of Section 5.4 . (B) must be solved using the techniques of Section \(5.3 .\) (C) can be solved using the techniques of either section.

Chapter 5

Mutual Funds In \(2015,\) the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield \(5 \%,\) and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield \(7 \% .^{6}\) You would like to invest a total of up to \(\$ 60,000\) and earn at least \(\$ 3,500\) in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). Find the corner points of the region.

Chapter 5

How would you use linear inequalities to describe the triangle with corner points \((0,0),(2,0),\) and (0,1)\(?\)

Chapter 5

In Exercises 9-22, solve the given standard minimization problem using duality. (You may already have seen some of these in earlier sections, but now you will be solving them using \(a\) different method.) $$ \begin{array}{ll} \text { Minimize } & c=3 s+2 t \\ \text { subject to } & s+2 t \geq 20 \\ & 2 s+t \geq 10 \\ & s \geq 0, t \geq 0 . \end{array} $$

Chapter 5

Given a minimization problem, when would you solve it by applying the simplex method to its dual, and when would you apply the simplex method to the minimization problem itself?

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