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

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.

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.

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

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.) $$ \begin{array}{ll} \text { Minimize } & c=3 s+2 t \\ \text { subject to } & s+2 t \geq 20 \\ & 2 s+t \geq 10 \\ & s \geq 0, t \geq 0 . \end{array} $$

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?