Maximize and minimize $p = 3 x - y$ subject to \[\begin{array} { l } x + y \geq 3 \\ x - y \leq 3 \\ x - y \geq - 3 \\ x \leq 12 , y \leq 12 \end{array}\]

A) Max: $p = 15$ , $x = 9$ , $y = 12$ , min: $p = - 3$ , $x = 0$ , $y = 3$ B) Max: $p = 27$ , $x = 12$ , $y = 9$ , Min: $p = 3$ , $x = 0$ , $y = 3$ C) Max: $p = 27$ , $x = 12$ , $y = 9$ , Min: $p = - 3$ , $x = 0$ , $y = 3$ D) the feasible region is empty E) the objective function is unbounded A) Max: $p = 15$ , $x = 9$ , $y = 12$ , min: $p = - 3$ , $x = 0$ , $y = 3$ B) Max: $p = 27$ , $x = 12$ , $y = 9$ , Min: $p = 3$ , $x = 0$ , $y = 3$ C) Max: $p = 27$ , $x = 12$ , $y = 9$ , Min: $p = - 3$ , $x = 0$ , $y = 3$ D) the feasible region is empty E) the objective function is unbounded

You are thinking of combining the three supplements in the table that gives you the maximum possible amount of creatine, but no more than 500 milligrams of alpha lipoic acid and 180 grams of carbohydrates. How many servings of each supplement should you combine to meet your specifications, and how much creatine will you get \[\begin{array} { | c | c | c | c | c | } \hline & \begin{array} { c } \text { Creatine } \\ ( \boldsymbol { g } ) \end{array} & \begin{array} { c } \text { Carbohydrates } \\ ( \boldsymbol { g } ) \end{array} & \begin{array} { c } \text { Taurine } \\ ( \boldsymbol { g } ) \end{array} & \begin{array} { c } \text { Alpha Lipoic } \\ \text { Acid } ( \mathrm { mg } ) \end{array} \\ \hline \begin{array} { c } \text { RiboForce HP } \\ \text { (EAS) } \end{array} & 5 & 15 & 1 & 0 \\ \hline \begin{array} { c } \text { Creatine Transport } \\ \text { (Kaizen) } \end{array} & 5 & 35 & 1 & 100 \\ \hline \begin{array} { c } \text { Pre-Load Creatine } \\ \text { (Optimum) } \end{array} & 6 & 35 & 1 & 25 \\ \hline \end{array}\]

A) use 12 servings of RiboForce HP and none of the others for a maximum of 60g creatine B) use 12 servings of Pre-Load Creatine and none of the others for a maximum of 60g creatine C) use 12 servings of Creatine Transport and none of the others for a maximum of 72g creatine D) use 12 servings of Pre-Load Creatine and none of the others for a maximum of 72g creatine E) use 12 servings of Creatine Transport and none of the others for a maximum of 60g creatine A) use 12 servings of RiboForce HP and none of the others for a maximum of 60g creatine B) use 12 servings of Pre-Load Creatine and none of the others for a maximum of 60g creatine C) use 12 servings of Creatine Transport and none of the others for a maximum of 72g creatine D) use 12 servings of Pre-Load Creatine and none of the others for a maximum of 72g creatine E) use 12 servings of Creatine Transport and none of the others for a maximum of 60g creatine

You have $450,000 and are considering investing in three municipal bond funds, Pimco, Fidelity Spartan, and Columbia Oregon. You have the following data: \[\begin{array} { | c | c | } \hline \text { Company } & \text { Yield } \\ \hline \text { PNF (Pimco NY) } & 7 \% \\ \hline \text { FDMMX (Fidelity Spartan Mass) } & 5 \% \\ \hline \text { CMBFX (Columbia Oregon) } & 4 \% \\ \hline \end{array}\] Your broker has made the following suggestions: At least 50 percent of your total investment should be in CMBFX. No more than 10 percent of your total investment should be in PNF. How much should you invest in each fund to maximize your anticipated returns while following your broker's advice $__________ in PNF, $__________ in FDMMX, and $__________ in CMBFX.

The answer of You have $450,000 and are considering investing...

Solve the standard minimization problem using duality. Minimize $C = 18 s + 29 t$ Subject to \[\begin{array} { l } 3 s + 2 t \geq 60 \\ 6 s + 3 t \geq 60 \\ s \geq 0 , t \geq 0 \end{array}\]

A) $C = 360$ , $s = 20$ , $t = 0$ B) $C = 580$ , $s = 0$ , $t = 20$ C) $C = 290$ , $s = 0$ , $t = 10$ D) $C = 180$ , $s = 10$ , $t = 0$ E) $C = 650$ , $s = 20$ , $t = 10$ A) $C = 360$ , $s = 20$ , $t = 0$ B) $C = 580$ , $s = 0$ , $t = 20$ C) $C = 290$ , $s = 0$ , $t = 10$ D) $C = 180$ , $s = 10$ , $t = 0$ E) $C = 650$ , $s = 20$ , $t = 10$

Solve the standard minimization problem using duality. Minimize $C = 18 s + 21 t$ subject to the following. \[\begin{array} { l } 3 s + 2 t \geq 48 \\ 7 s + 3 t \geq 56 \\ s \geq 0 , t \geq 0 \end{array}\] \[C =\] __________ \[s =\] __________ \[t =\] __________

The answer of Solve the standard minimization problem using duality....

Maximize $p = 3 x + 5 y + z$ Subject to \[\begin{aligned} 2 x - 6 y + 2 z & \leq 20 \\ x + 3 y - 4 z & \leq 11 \\ x \geq 0 , y \geq 0 , z & \geq 0 \end{aligned}\]

A) $p = 116$ , $x = 9$ , $y = 14$ , $z = 13$ B) $p = 116$ , $x = 13$ , $y = 9$ , $z = 14$ C) $p = 116$ , $x = 14$ , $y = 9$ , $z = 13$ D) $p = 116$ , $x = 14$ , $y = 13$ , $z = 9$ E) no solution A) $p = 116$ , $x = 9$ , $y = 14$ , $z = 13$ B) $p = 116$ , $x = 13$ , $y = 9$ , $z = 14$ C) $p = 116$ , $x = 14$ , $y = 9$ , $z = 13$ D) $p = 116$ , $x = 14$ , $y = 13$ , $z = 9$ E) no solution

Maximize $p = 7 x + 9 y$ subject to the following (using the simplex method). \[\begin{aligned} 9 x + 8 y & \leq 144 \\ x + y & \geq 8 \\ 8 x + 9 y & \leq 144 \\ x \geq 0 , y & \geq 0 \end{aligned}\]

A) $p = 112$ , $x = 16$ , $y = 0$ B) $p = 144$ , $x = 0$ , $y = 16$ C) $p = 56$ , $x = 8$ , $y = 0$ D) $p = 72$ , $x = 0$ , $y = 8$ E) no solution A) $p = 112$ , $x = 16$ , $y = 0$ B) $p = 144$ , $x = 0$ , $y = 16$ C) $p = 56$ , $x = 8$ , $y = 0$ D) $p = 72$ , $x = 0$ , $y = 8$ E) no solution

Minimize $c = 2 x + y + 3 z$ Subject to \[\begin{aligned} x + y + z & \geq 150 \\ 2 x + y & \geq 30 \\ y + z & \geq 40 \\ x \geq 0 , y \geq 0 , z & \geq 0 \end{aligned}\]

A) $c = 450$ , $x = 0$ , $y = 0$ , $z = 150$ B) $c = 300$ , $x = 150$ , $y = 0$ , $z = 0$ C) $c = 150$ , $x = 0$ , $y = 150$ , $z = 0$ D) $c = 30$ , $x = 0$ , $y = 30$ , $z = 0$ E) no solution A) $c = 450$ , $x = 0$ , $y = 0$ , $z = 150$ B) $c = 300$ , $x = 150$ , $y = 0$ , $z = 0$ C) $c = 150$ , $x = 0$ , $y = 150$ , $z = 0$ D) $c = 30$ , $x = 0$ , $y = 30$ , $z = 0$ E) no solution

Solve the standard minimization problem using duality. Minimize $c = 0.4 s + 0.6 t$ Subject to \[\begin{array} { l } 0.2 s + 0.1 t \geq 1 \\ 0.15 s + 0.3 t \geq 1.5 \\ 10 s + 10 t \geq 80 \\ s \geq 0 , t \geq 0 \end{array}\]

A) $c = 3.6$ , $s = 6$ , $t = 2$ B) $c = 2.8$ , $s = 6$ , $t = 2$ C) $c = 1.2$ , $s = 6$ , $t = 2$ D) $c = 4.4$ , $s = 2$ , $t = 6$ E) $c = 2.8$ , $s = 2$ , $t = 6$ A) $c = 3.6$ , $s = 6$ , $t = 2$ B) $c = 2.8$ , $s = 6$ , $t = 2$ C) $c = 1.2$ , $s = 6$ , $t = 2$ D) $c = 4.4$ , $s = 2$ , $t = 6$ E) $c = 2.8$ , $s = 2$ , $t = 6$

Exam 6: Linear Programming

Your publishing company is about to start a promotional blitz for its new book, Physics for the Liberal Arts. You have 30 salespeople stationed in Chicago and 5 in Denver. You would like to fly at most 5 into Los Angeles and at most 20 into New York. A round-trip plane flight from Chicago to LA costs $195; from Chicago to NY costs $182; from Denver to LA costs $395; and from Denver to NY costs $166. You want to spend at most $4,535 on plane flights. How many salespeople should you fly from each of Chicago and Denver to each of LA and NY to have the most salespeople on the road people from Chicago to LA, people from Chicago to NY, people from Denver to LA, and people from Denver to NY.

(Short Answer)

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Question 121

Your portfolio manager has suggested two high-yielding stocks: The Altria Group (MO) and Reynolds America (RAI). MO shares cost $50, yield 4.5% in dividends, and have a risk index of 2.0 per share. RAI shares cost $55, yield 5% in dividends, and have a risk index of 3.0 per share. You have up to $15,750 to invest and would like to earn at least $722.5 in dividends. ? How many shares (to the nearest whole number) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio ? If no optimal solution exists enter no solution in each box. ? Number of shares of MO = ? Number of shares of RAI = ? What is the minimum total risk index ? $ __

(Short Answer)

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Question 122

Maximize and minimize $p = 3 x - y$ subject to x+y\geq3 x-y\leq3 x-y\geq-3 x\leq12,y\leq12

(Multiple Choice)

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Question 123

every linear programming problem with a bounded feasible region has an optimal solution.

(True/False)

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Question 124

You are thinking of combining the three supplements in the table that gives you the maximum possible amount of creatine, but no more than 500 milligrams of alpha lipoic acid and 180 grams of carbohydrates. How many servings of each supplement should you combine to meet your specifications, and how much creatine will you get Creatine ( ) Carbohydrates ( ) Taurine ( ) Alpha Lipoic Acid () RiboForce HP (EAS) 5 15 1 0 Creatine Transport (Kaizen) 5 35 1 100 Pre-Load Creatine (Optimum) 6 35 1 25

(Multiple Choice)

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Question 125

You have $450,000 and are considering investing in three municipal bond funds, Pimco, Fidelity Spartan, and Columbia Oregon. You have the following data: Company Yield PNF (Pimco NY) 7\% FDMMX (Fidelity Spartan Mass) 5\% CMBFX (Columbia Oregon) 4\% Your broker has made the following suggestions: At least 50 percent of your total investment should be in CMBFX. No more than 10 percent of your total investment should be in PNF. How much should you invest in each fund to maximize your anticipated returns while following your broker's advice $ in PNF, $ in FDMMX, and $__ in CMBFX.

(Essay)

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Question 126

Solve the standard minimization problem using duality. Minimize $C = 18 s + 29 t$ Subject to 3s+2t\geq60 6s+3t\geq60 s\geq0,t\geq0

(Multiple Choice)

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Question 127

Solve the games with the given payoff matrix. $\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]$

(Multiple Choice)

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Question 128

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 1,100 eggs and 2,100 cups of cream. Draw the feasible region showing the number of quarts of vanilla and number of quarts of mocha that can be produced. Find the corner points of the region. Let the number of quarts of Creamy Vanilla be x, and the number of quarts of Continental Mocha be y.

(Multiple Choice)

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Question 129

Solve the standard minimization problem using duality. Minimize $C = 18 s + 21 t$ subject to the following. 3s+2t\geq48 7s+3t\geq56 s\geq0,t\geq0 $C =$ $s =$ $t =$ __

(Short Answer)

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Question 130

Solve the standard minimization problem using duality. Minimize $c = 6 s + 2 t$ subject to s+t\geq9 6s+t\geq24 s\geq0,t\geq0 After using the simplex method for dual problem to arrive at the tableau below, what is the maximum value for c $\quad \quad x\quad y\quad z \quad w \quad c$ $\left[ \begin{array} { c c c c c } 0&1&\frac{1}{5}&\frac{1}{-5}&0\\\frac{4}{5}\\1&0&\frac{1}{-5}&\frac{6}{5}&0\\\frac{6}{5}\\0&0&3&6&1\\30\end{array} \right]$

(Essay)

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Question 131

Minimize $c = 5.45 x + y + 1.5 z + w$ subject to 5.12x-y+w \geq1,500 z+w \geq3,000 1.12x+y \leq500 x\geq0,y\geq0,z\geq0,w \geq0 If there is no solution, do not fill the fields. $c =$ $x =$ $y =$ $z =$ $w ^ { \prime } =$ __

(Short Answer)

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Question 132

Maximize $p = 3 x + 5 y + z$ Subject to 2x-6y+2z \leq20 x+3y-4z \leq11 x\geq0,y\geq0,z \geq0

(Multiple Choice)

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Question 133

Maximize $p = 7 x + 9 y$ subject to the following (using the simplex method). 9x+8y \leq144 x+y \geq8 8x+9y \leq144 x\geq0,y \geq0

(Multiple Choice)

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Question 134

Minimize $c = 2 x + y + 3 z$ Subject to x+y+z \geq150 2x+y \geq30 y+z \geq40 x\geq0,y\geq0,z \geq0

(Multiple Choice)

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Question 135

The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern History, and the department chairperson is trying to decide how many sections of each to offer this semester. They may offer up to 40 sections total, up to 5,000 students would like to take a course, and there are 50 professors to teach them (no student will take more than one history course, and no professor will teach more than one section). Sections of Ancient History have 100 students each, sections of Medieval History have 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. Ancient History nets the university $10,000 per section, Medieval nets $ 20,000, and Modern History nets $30,000 per section. How many sections of each course should the department offer in order to generate the largest profit The department should offer section(s) of Ancient History, section(s) of Medieval History, and section(s) of Modern History. What is the largest profit possible The profit is $. Will there be any unused time slots, any students who did not get into classes, or any professors without anything to teach There will be student(s) without classes, professor(s) without anything to teach, and __ unused time slots.

(Short Answer)

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Question 136

Select the correct graph of the given system of inequalities. $\left\{ \begin{aligned}4 x - 7 y & \geq - 24 \\x + 3 y & \geq 5 \\x & \geq 0 \\y & \geq 0\end{aligned} \right.$

(Multiple Choice)

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Question 137

You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1,400 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 3 units each, and you can spare at most 1,600 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit ? You should purchase calculus text(s), history text(s) and marketing text(s). ? What is the maximum profit the program can make in a semester ? The maximum profit is $ per semester.

(Short Answer)

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Question 138

Solve the standard minimization problem using duality. Minimize $c = 0.4 s + 0.6 t$ Subject to 0.2s+0.1t\geq1 0.15s+0.3t\geq1.5 10s+10t\geq80 s\geq0,t\geq0

(Multiple Choice)

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Question 139

Graph the solution set to the inequality. Label coordinates of all corner points (if any). $x - 6 y \geq 12$

(Multiple Choice)

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Question 140

Maximize and minimize $p = 3 x - y$ subject to x+y\geq3 x-y\leq3 x-y\geq-3 x\leq12,y\leq12

every linear programming problem with a bounded feasible region has an optimal solution.

Solve the standard minimization problem using duality. Minimize $C = 18 s + 29 t$ Subject to 3s+2t\geq60 6s+3t\geq60 s\geq0,t\geq0

Solve the games with the given payoff matrix. $\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]$

Solve the standard minimization problem using duality. Minimize $C = 18 s + 21 t$ subject to the following. 3s+2t\geq48 7s+3t\geq56 s\geq0,t\geq0 $C =$ $s =$ $t =$ __

Minimize $c = 5.45 x + y + 1.5 z + w$ subject to 5.12x-y+w \geq1,500 z+w \geq3,000 1.12x+y \leq500 x\geq0,y\geq0,z\geq0,w \geq0 If there is no solution, do not fill the fields. $c =$ $x =$ $y =$ $z =$ $w ^ { \prime } =$ __

Maximize $p = 3 x + 5 y + z$ Subject to 2x-6y+2z \leq20 x+3y-4z \leq11 x\geq0,y\geq0,z \geq0

Maximize $p = 7 x + 9 y$ subject to the following (using the simplex method). 9x+8y \leq144 x+y \geq8 8x+9y \leq144 x\geq0,y \geq0

Minimize $c = 2 x + y + 3 z$ Subject to x+y+z \geq150 2x+y \geq30 y+z \geq40 x\geq0,y\geq0,z \geq0

Select the correct graph of the given system of inequalities. $\left\{ \begin{aligned}4 x - 7 y & \geq - 24 \\x + 3 y & \geq 5 \\x & \geq 0 \\y & \geq 0\end{aligned} \right.$

Solve the standard minimization problem using duality. Minimize $c = 0.4 s + 0.6 t$ Subject to 0.2s+0.1t\geq1 0.15s+0.3t\geq1.5 10s+10t\geq80 s\geq0,t\geq0

Graph the solution set to the inequality. Label coordinates of all corner points (if any). $x - 6 y \geq 12$

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Sets and Counting

Probability

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Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

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Exam 6: Linear Programming

Maximize and minimize p=3x−yp = 3 x - yp=3x−y subject to x+y\geq3 x-y\leq3 x-y\geq-3 x\leq12,y\leq12

​every linear programming problem with a bounded feasible region has an optimal solution.

Solve the standard minimization problem using duality. Minimize C=18s+29tC = 18 s + 29 tC=18s+29t Subject to 3s+2t\geq60 6s+3t\geq60 s\geq0,t\geq0

Solve the games with the given payoff matrix. [1−1201201011020−22]\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]​1102​−1210​201−2​0102​​

Solve the standard minimization problem using duality. Minimize C=18s+21tC = 18 s + 21 tC=18s+21t subject to the following. ​ 3s+2t\geq48 7s+3t\geq56 s\geq0,t\geq0 ​ C=C =C= __________ ​ s=s =s= __________ ​ t=t =t= __________

Maximize p=3x+5y+zp = 3 x + 5 y + zp=3x+5y+z Subject to 2x-6y+2z \leq20 x+3y-4z \leq11 x\geq0,y\geq0,z \geq0

Maximize p=7x+9yp = 7 x + 9 yp=7x+9y subject to the following (using the simplex method). 9x+8y \leq144 x+y \geq8 8x+9y \leq144 x\geq0,y \geq0

Minimize c=2x+y+3zc = 2 x + y + 3 zc=2x+y+3z Subject to x+y+z \geq150 2x+y \geq30 y+z \geq40 x\geq0,y\geq0,z \geq0

Select the correct graph of the given system of inequalities. {4x−7y≥−24x+3y≥5x≥0y≥0\left\{ \begin{aligned}4 x - 7 y & \geq - 24 \\x + 3 y & \geq 5 \\x & \geq 0 \\y & \geq 0\end{aligned} \right.⎩⎨⎧​4x−7yx+3yxy​≥−24≥5≥0≥0​

Solve the standard minimization problem using duality. Minimize c=0.4s+0.6tc = 0.4 s + 0.6 tc=0.4s+0.6t Subject to 0.2s+0.1t\geq1 0.15s+0.3t\geq1.5 10s+10t\geq80 s\geq0,t\geq0

Graph the solution set to the inequality. Label coordinates of all corner points (if any). x−6y≥12x - 6 y \geq 12x−6y≥12

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Maximize and minimize $p = 3 x - y$ subject to x+y\geq3 x-y\leq3 x-y\geq-3 x\leq12,y\leq12

every linear programming problem with a bounded feasible region has an optimal solution.

Solve the standard minimization problem using duality. Minimize $C = 18 s + 29 t$ Subject to 3s+2t\geq60 6s+3t\geq60 s\geq0,t\geq0

Solve the games with the given payoff matrix. $\left[ \begin{array} { c c c c } 1 & - 1 & 2 & 0 \\1 & 2 & 0 & 1 \\0 & 1 & 1 & 0 \\2 & 0 & - 2 & 2\end{array} \right]$

Solve the standard minimization problem using duality. Minimize $C = 18 s + 21 t$ subject to the following. 3s+2t\geq48 7s+3t\geq56 s\geq0,t\geq0 $C =$ $s =$ $t =$ __

Maximize $p = 3 x + 5 y + z$ Subject to 2x-6y+2z \leq20 x+3y-4z \leq11 x\geq0,y\geq0,z \geq0

Maximize $p = 7 x + 9 y$ subject to the following (using the simplex method). 9x+8y \leq144 x+y \geq8 8x+9y \leq144 x\geq0,y \geq0

Minimize $c = 2 x + y + 3 z$ Subject to x+y+z \geq150 2x+y \geq30 y+z \geq40 x\geq0,y\geq0,z \geq0

Select the correct graph of the given system of inequalities. $\left\{ \begin{aligned}4 x - 7 y & \geq - 24 \\x + 3 y & \geq 5 \\x & \geq 0 \\y & \geq 0\end{aligned} \right.$

Solve the standard minimization problem using duality. Minimize $c = 0.4 s + 0.6 t$ Subject to 0.2s+0.1t\geq1 0.15s+0.3t\geq1.5 10s+10t\geq80 s\geq0,t\geq0

Graph the solution set to the inequality. Label coordinates of all corner points (if any). $x - 6 y \geq 12$