The University's employee credit union has $4 million available for loans in the coming year. As VP in charge of finances, you must decide how much capital to allocate to each of four different kinds of loans, as shown in the table. \[\begin{array} { | c | c | } \hline \text { Type of Loan } & \begin{array} { c } \text { Annual Rate of } \\ \text { Return } \end{array} \\ \hline \text { Automobile } & 8 \% \\ \hline \text { Furniture } & 10 \% \\ \hline \text { Signature } & 12 \% \\ \hline \text { Other secured } & 10 \% \\ \hline \end{array}\] State laws and credit union policies impose the following restrictions: Signature loans may not exceed 10 percent of the total investment of funds. Furniture loans plus other secured loans may not exceed automobile loans. How much should you allocate to each type of loan to maximize the annual return

A) allocate $1,800,000 to automobile loans, $400,000 to signature loans, $1,800,000 to furniture loans and no allocation to other secured loans B) allocate $1,800,000 to automobile loans, $400,000 to signature loans, no allocation to furniture loans and $1,800,000 other secured loans C) allocate $400,000 to automobile loans, $1,800,000 to signature loans, and $1,800,000 to any combination of furniture loans and other secured loans D) allocate $1,800,000 to automobile loans, $400,000 to signature loans, and $1,800,000 to any combination of furniture loans and other secured loans E) allocate $1,800,000 to automobile loans, $400,000 to signature loans, and $400,000 to any combination of furniture loans and other secured loans A) allocate $1,800,000 to automobile loans, $400,000 to signature loans, $1,800,000 to furniture loans and no allocation to other secured loans B) allocate $1,800,000 to automobile loans, $400,000 to signature loans, no allocation to furniture loans and $1,800,000 other secured loans C) allocate $400,000 to automobile loans, $1,800,000 to signature loans, and $1,800,000 to any combination of furniture loans and other secured loans D) allocate $1,800,000 to automobile loans, $400,000 to signature loans, and $1,800,000 to any combination of furniture loans and other secured loans E) allocate $1,800,000 to automobile loans, $400,000 to signature loans, and $400,000 to any combination of furniture loans and other secured loans

Minimize $c = 5 x + 8 y$ subject to the following (using the simplex method). \[\begin{array} { l } 7 x + 3 y \geq 30 \\ 2 x + 3 y \geq 12 \\ x \geq 0 , y \geq 0 \end{array}\] $c =$ __________ $x =$ __________ $y =$ __________

The answer of Minimize \(c = 5 x + 8...

You are thinking of combining Cell-Tech and Riboforce HP to obtain a 10-day supply that provides at least 50 grams of creatine and at least 8 grams of taurine, but no more than 600 grams of carbohydrates and no more than 800 milligrams of alpha lipoic acid. Use the data on bodybuilding supplements. (Figures shown correspond to a single serving.) \[\begin{array} { | l | l | l | l | l | l | } \hline & \begin{array} { l } \text { Creatine } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Carbohydrates } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Taurine } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Alpha Lipoic } \\ \text { Acid } ( \mathrm { mg } ) \end{array} & \begin{array} { l } \text { Cost } \\ ( \mathrm { S } ) \end{array} \\ \hline \begin{array} { l } \text { Cell-Tech } \\ \text { MuscleTech) } \end{array} & 10 & 75 & 2 & 200 & 2.20 \\ \hline \begin{array} { l } \text { RiboForce HP } \\ \text { (EAS) } \end{array} & 5 & 15 & 1 & 0 & 1.60 \\ \hline \end{array}\] How many servings of each supplement should you combine to meet your specifications at the least cost

A) 4 servings of Cell-Tech and 20 servings of Riboforce HP B) 4 servings of Cell-Tech and 2 servings of Riboforce HP C) 0 servings of Cell-Tech and 40 servings of Riboforce HP D) 0 servings of Cell-Tech and 10 servings of Riboforce HP E) no solution A) 4 servings of Cell-Tech and 20 servings of Riboforce HP B) 4 servings of Cell-Tech and 2 servings of Riboforce HP C) 0 servings of Cell-Tech and 40 servings of Riboforce HP D) 0 servings of Cell-Tech and 10 servings of Riboforce HP E) no solution

Solve the linear programming problem. Minimize $C = - 3 x - 5 y$ subject to $\begin{array} { l } 2 x + 3 y \leq 12 \\ 7 x - 6 y \leq 30 \\ x \geq 0 , y \geq 0 \end{array}$ $x =$ __________ $y =$ __________ $C =$ __________

The answer of Solve the linear programming problem. Minimize \(C =...

Maximize $p = x + 2 y$ Subject to \[\begin{aligned} x + y & \leq 20 \\ y & \geq 8 \\ 2 x - y & \geq 0 \\ x \geq 0 , y & \geq 0 \end{aligned}\]

A) $p = 80$ , $x = 40$ , $y = 20$ B) $p = 100$ , $x = 20$ , $y = 40$ C) $p = \frac { 80 } { 3 }$ , $x = \frac { 40 } { 3 }$ , $y = \frac { 20 } { 3 }$ D) $p = \frac { 100 } { 3 }$ , $x = \frac { 20 } { 3 }$ , $y = \frac { 40 } { 3 }$ E) no solution A) $p = 80$ , $x = 40$ , $y = 20$ B) $p = 100$ , $x = 20$ , $y = 40$ C) $p = \frac { 80 } { 3 }$ , $x = \frac { 40 } { 3 }$ , $y = \frac { 20 } { 3 }$ D) $p = \frac { 100 } { 3 }$ , $x = \frac { 20 } { 3 }$ , $y = \frac { 40 } { 3 }$ E) no solution

Solve the standard minimization problem using duality. \[\begin{array} { l } \text { Minimize } ^ { c = 3 s + 3 t + 3 u } \\ 3 s + 2 t + u \geq 150 \\ 2 s + t + 3 u \geq 150 \\ \text { subject to } s + 3 t + 2 u \geq 150 \\ s \geq 0 , t \geq 0 , u \geq 0 \\ \end{array}\] If you have several solutions, select one of them.

A) $c = 90$ , $s = 37.5$ , $t = 0$ , $u = 37.5$ B) $c = 225$ , $s = 25$ , $t = 25$ , $u = 25$ C) $c = 135$ , $s = 15$ , $t = 15$ , $u = 15$ D) $c = 180$ , $s = 20$ , $t = 20$ , $u = 20$ E) $c = 225$ , $s = 10$ , $t = 10$ , $u = 10$ A) $c = 90$ , $s = 37.5$ , $t = 0$ , $u = 37.5$ B) $c = 225$ , $s = 25$ , $t = 25$ , $u = 25$ C) $c = 135$ , $s = 15$ , $t = 15$ , $u = 15$ D) $c = 180$ , $s = 20$ , $t = 20$ , $u = 20$ E) $c = 225$ , $s = 10$ , $t = 10$ , $u = 10$

Maximize $p = x + 2 y$ subject to \[\begin{aligned} x + y & \leq 25 \\ y & \geq 3 \\ 2 x - y & \geq 0 \\ x \geq 0 , y & \geq 0 \end{aligned}\] Please enter your answer as three numbers, separated by commas in the order p, x, y. If there is no solution, enter no solution.

The answer of Maximize $p = x + 2 y$...

If x dollars is invested in a company that controls, say, 30 percent of the market with 5 brand-names, then $0.3 x$ is a measure of market exposure and $5 x$ is a measure of brand-name exposure. Now suppose you are a broker at a large securities firm, and one of your clients would like to invest up to $100,000 in recording industry stocks. You decide to recommend a combination of stocks in four of the world's largest companies: Warner Music, Universal Music, Sony, and EMI. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Warner Music } & \text { Universal Music } & \text { Sony } & \text { EMI } \\ \hline \text { Market Share } & 12 \% & 20 \% & 20 \% & 15 \% \\ \hline \begin{array} { c } \text { Number of } \\ \text { brand-names } \end{array} & 8 & 20 & 10 & 15 \\ \hline \end{array}\] You wanted your client to maximize his total market exposure but limit his brand-name exposure to 2 million or less (representing an average of 20 labels or fewer per company), and still invest at least 20 percent of the total in Universal. How much should you advise your client to invest in each company

A) $20,000 in Warner Music, $80,000 in Sony, and no investment in Universal Music and EMI B) $80,000 in Warner Music, $20,000 in EMI, and no investment in Universal Music and Sony C) $20,000 in Universal Music, $80,000 in Sony, and no investment in Warner Music and EMI D) $80,000 in Warner Music, $20,000 in Sony, and no investment in Universal Music and EMI E) $80,000 in Universal Music, $20,000 in Sony, and no investment in Warner Music and EMI A) $20,000 in Warner Music, $80,000 in Sony, and no investment in Universal Music and EMI B) $80,000 in Warner Music, $20,000 in EMI, and no investment in Universal Music and Sony C) $20,000 in Universal Music, $80,000 in Sony, and no investment in Warner Music and EMI D) $80,000 in Warner Music, $20,000 in Sony, and no investment in Universal Music and EMI E) $80,000 in Universal Music, $20,000 in Sony, and no investment in Warner Music and EMI

Minimize $c = 5.45 x + y + 1.5 z + w$ Subject to \[\begin{aligned} 5.12 x - y + w & \geq 1,500 \\ z + w & \geq 1,500 \\ 1.12 x + y & \leq 1,000 \\ x \geq 0 , y \geq 0 , z & \geq 0 \end{aligned}\]

A) $c = 1,500$ , $x = 0$ , $y = 1,500$ , $z = 0$ , $w = 0$ B) $c = 1,500$ , $x = 0$ , $y = 0$ , $z = 0$ , $w = 1,500$ C) $c = 1,500$ , $x = 0$ , $y = 0$ , $z = 1,500$ , $w = 0$ D) $c = 8,175$ , $x = 1,500$ , $y = 0$ , $z = 0$ , $w = 0$ E) $c = 2,250$ , $x = 0$ , $y = 0$ , $z = 1,500$ , $w = 0$ A) $c = 1,500$ , $x = 0$ , $y = 1,500$ , $z = 0$ , $w = 0$ B) $c = 1,500$ , $x = 0$ , $y = 0$ , $z = 0$ , $w = 1,500$ C) $c = 1,500$ , $x = 0$ , $y = 0$ , $z = 1,500$ , $w = 0$ D) $c = 8,175$ , $x = 1,500$ , $y = 0$ , $z = 0$ , $w = 0$ E) $c = 2,250$ , $x = 0$ , $y = 0$ , $z = 1,500$ , $w = 0$

You are thinking of combining Cell-Tech and Creatine Transport to obtain a 10-day supply that provides at least 90 grams of creatine and at least 10 grams of taurine, but no more than 675 grams of Carbohydrates and no more than 2,500 milligrams of alpha lipoic acid. Use the data on bodybuilding supplements. (Figures shown correspond to a single serving.) \[\begin{array} { | l | l | l | l | l | l | } \hline & \begin{array} { l } \text { Creatine } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Carbohydrates } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Taurine } \\ ( \mathrm { g } ) \end{array} & \begin{array} { l } \text { Alpha Lipoic } \\ \text { Acid } ( \mathrm { mg } ) \end{array} & \begin{array} { l } \text { Cost } \\ ( \$ ) \end{array} \\ \hline \text { Cell-Tech } & 10 & 75 & 2 & 200 & 2.20 \\ \text { (MuscleTech) } & & & \\ \hline \begin{array} { l } \text { Creatine } \\ \text { Transport } \\ \text { (Kaizen) } \end{array} & 5 & 35 &1 & 100 & 0.60 \\ \hline \end{array}\] How many servings of each supplement should you combine to meet your specifications at the least cost

A) 5 servings of Cell-Tech and 0 servings of Creatine Transport B) 0 servings of Cell-Tech and 18 servings of Creatine Transport C) 0 servings of Cell-Tech and 10 servings of Creatine Transport D) 9 servings of Cell-Tech and 0 servings of Creatine Transport E) no solution A) 5 servings of Cell-Tech and 0 servings of Creatine Transport B) 0 servings of Cell-Tech and 18 servings of Creatine Transport C) 0 servings of Cell-Tech and 10 servings of Creatine Transport D) 9 servings of Cell-Tech and 0 servings of Creatine Transport E) no solution

Exam 6: Linear Programming

Maximize $p = 1.2 x + 1.1 y$ over the region defined by the inequalities. Round your answer to one decimal place. $\left\{ \begin{array} { c } 7 x + 6 y \leq 84 \\x + y \leq 13 \\x \geq 0 , y \geq 0\end{array} \right\}$ Max: $p =$ __________

(Short Answer)

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Question 81

The Marketing Club at your college has decided to raise funds by selling three types of T-shirt: one with a single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. The club feels that it can sell up to 400 T-shirts. "Ordinary" T-shirts will cost the club $6 each, "fancy" T-shirts $8 each, and "very fancy" T-shirts $10 each, and the club has a total purchasing budget of $4,000. It will sell "ordinary" T-shirts at a profit of $4 each, "fancy" T-shirts at a profit of $5 each, and "very fancy" T-shirts at a profit of $4 each. How many of each kind of T-shirt should the club order to maximize profit What is the maximum profit the club can make ?

(Multiple Choice)

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Question 82

The University's employee credit union has $4 million available for loans in the coming year. As VP in charge of finances, you must decide how much capital to allocate to each of four different kinds of loans, as shown in the table. Type of Loan Annual Rate of Return Automobile 8\% Furniture 10\% Signature 12\% Other secured 10\% State laws and credit union policies impose the following restrictions: Signature loans may not exceed 10 percent of the total investment of funds. Furniture loans plus other secured loans may not exceed automobile loans. How much should you allocate to each type of loan to maximize the annual return

(Multiple Choice)

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Question 83

Maximize $p = 2 x + 3 y + 1.1 z + 4 w$ Subject to 1.2x+y+z+w \leq42 2.2x+y-z-w \geq15 1.2x+y+z+1.2w \geq11.5 x\geq0,y\geq0,z\geq0,w \geq0 Round all answers to two decimal places.

(Multiple Choice)

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Question 84

Minimize $c = 5 x + 8 y$ subject to the following (using the simplex method). 7x+3y\geq30 2x+3y\geq12 x\geq0,y\geq0 $c =$ $x =$ $y =$ __

(Short Answer)

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Question 85

Fancy Pineapple produces pineapple juice and canned pineapple rings. This year the company anticipates a demand of at least 10,000 pints of pineapple juice and 500 cans of pineapple rings. Each pint of pineapple juice requires 2 pineapples, and each can of pineapple rings requires 1 pineapple. The company anticipates using at least 5,000 pineapples for these products. Each pint of pineapple juice costs the company 20 cents to produce, and each can of pineapple rings costs 50 cents to produce. How many pints of pineapple juice and cans of pineapple rings should Fancy Pineapple produce to meet the demand and minimize total costs ?

(Multiple Choice)

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Question 86

Which system does the graph satisfy

(Multiple Choice)

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Question 87

You are thinking of combining Cell-Tech and Riboforce HP to obtain a 10-day supply that provides at least 50 grams of creatine and at least 8 grams of taurine, but no more than 600 grams of carbohydrates and no more than 800 milligrams of alpha lipoic acid. Use the data on bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine () Carbohydrates () Taurine () Alpha Lipoic Acid () Cost () Cell-Tech MuscleTech) 10 75 2 200 2.20 RiboForce HP (EAS) 5 15 1 0 1.60 How many servings of each supplement should you combine to meet your specifications at the least cost

(Multiple Choice)

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Question 88

Solve the linear programming problem. Minimize $C = - 3 x - 5 y$ subject to 2x+3y\leq12 7x-6y\leq30 x\geq0,y\geq0 $x =$ $y =$ $C =$ __

(Short Answer)

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Question 89

Maximize $p = x + 2 y$ Subject to x+y \leq20 y \geq8 2x-y \geq0 x\geq0,y \geq0

(Multiple Choice)

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Question 90

Solve the standard minimization problem using duality. 3s+2t+u\geq150 2s+t+3u\geq150 subject to s+3t+2u\geq150 s\geq0,t\geq0,u\geq0 If you have several solutions, select one of them.

(Multiple Choice)

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Question 91

Maximize $p = x + 2 y$ subject to x+y \leq25 y \geq3 2x-y \geq0 x\geq0,y \geq0 Please enter your answer as three numbers, separated by commas in the order p, x, y. If there is no solution, enter no solution.

(Essay)

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Question 92

If x dollars is invested in a company that controls, say, 30 percent of the market with 5 brand-names, then $0.3 x$ is a measure of market exposure and $5 x$ is a measure of brand-name exposure. Now suppose you are a broker at a large securities firm, and one of your clients would like to invest up to $100,000 in recording industry stocks. You decide to recommend a combination of stocks in four of the world's largest companies: Warner Music, Universal Music, Sony, and EMI. Warner Music Universal Music Sony EMI Market Share 12\% 20\% 20\% 15\% Number of brand-names 8 20 10 15 You wanted your client to maximize his total market exposure but limit his brand-name exposure to 2 million or less (representing an average of 20 labels or fewer per company), and still invest at least 20 percent of the total in Universal. How much should you advise your client to invest in each company

(Multiple Choice)

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Question 93

Minimize $c = 5.45 x + y + 1.5 z + w$ Subject to 5.12x-y+w \geq1,500 z+w \geq1,500 1.12x+y \leq1,000 x\geq0,y\geq0,z \geq0

(Multiple Choice)

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Question 94

Solve the standard minimization problem using duality. Minimize $c = 5 s + 4 t$ subject to 3s+t\geq30 s+t\geq20 s+3t\geq30 s\geq0,t\geq0 $c =$ $s =$ $t =$ ___

(Short Answer)

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Question 95

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 1,100 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 1,200 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 What is the maximum profit the program can make in a semester ?

(Multiple Choice)

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Question 96

Solve the games with the given payoff matrix. $P = \left[ \begin{array} { l l l } - 3 & - 5 & - 2 \\- 3 & - 2 & - 4 \\- 4 & - 3 & - 3\end{array} \right]$

(Multiple Choice)

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Question 97

Safety-Kleen operates the world's largest oil refinery at Elgin, Illinois. You have been hired by the company to determine how to allocate its intake of up to 70 million gallons of used oil to its three refinery processes: A, B, and C. You are told that electricity costs for process A amount to $150,000 per million gallons treated, while for processes B and C, the costs are respectively $100,000 and $50,000 per million gallons treated. Process A can recover 60 percent of the used oil, process B can recover 55 percent, and process C can recover only 50 percent. Assuming a revenue of $4 million per million gallons of recovered oil and an annual electrical budget of $4.9 million, how much used oil would you allocate to each process in order to maximize total revenues Allocate million gals to process A, million gals to process B and __ million gals to process C.

(Short Answer)

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Question 98

Oz makes lion food out of giraffe and gazelle meat. Giraffe meat has 18 grams of protein and 36 grams of fat per pound, while gazelle meat has 36 grams of protein and 18 grams of fat per pound. A batch of lion food must contain at least 36,000 grams of protein and 54,000 grams of fat. Giraffe meat costs $2/pound and gazelle meat costs $4/pound. How many pounds of each should go into each batch of lion food in order to minimize costs Please round the answers to the nearest pound. pound(s) of giraffe meat and pound(s) of gazelle. What are the shadow costs of protein and fat Please round the answers to the nearest cent. cents per gram of protein and cents per gram of fat.

(Short Answer)

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Question 99

You are thinking of combining Cell-Tech and Creatine Transport to obtain a 10-day supply that provides at least 90 grams of creatine and at least 10 grams of taurine, but no more than 675 grams of Carbohydrates and no more than 2,500 milligrams of alpha lipoic acid. Use the data on bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine () Carbohydrates () Taurine () Alpha Lipoic Acid () Cost (\ ) Cell-Tech 10 75 2 200 2.20 (MuscleTech) Creatine Transport (Kaizen) 5 35 1 100 0.60 How many servings of each supplement should you combine to meet your specifications at the least cost

(Multiple Choice)

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Question 100

Maximize $p = 1.2 x + 1.1 y$ over the region defined by the inequalities. Round your answer to one decimal place. $\left\{ \begin{array} { c } 7 x + 6 y \leq 84 \\x + y \leq 13 \\x \geq 0 , y \geq 0\end{array} \right\}$ Max: $p =$ __________

Maximize $p = 2 x + 3 y + 1.1 z + 4 w$ Subject to 1.2x+y+z+w \leq42 2.2x+y-z-w \geq15 1.2x+y+z+1.2w \geq11.5 x\geq0,y\geq0,z\geq0,w \geq0 Round all answers to two decimal places.

Minimize $c = 5 x + 8 y$ subject to the following (using the simplex method). 7x+3y\geq30 2x+3y\geq12 x\geq0,y\geq0 $c =$ $x =$ $y =$ __

Which system does the graph satisfy

Solve the linear programming problem. Minimize $C = - 3 x - 5 y$ subject to 2x+3y\leq12 7x-6y\leq30 x\geq0,y\geq0 $x =$ $y =$ $C =$ __

Maximize $p = x + 2 y$ Subject to x+y \leq20 y \geq8 2x-y \geq0 x\geq0,y \geq0

Solve the standard minimization problem using duality. 3s+2t+u\geq150 2s+t+3u\geq150 subject to s+3t+2u\geq150 s\geq0,t\geq0,u\geq0 If you have several solutions, select one of them.

Maximize $p = x + 2 y$ subject to x+y \leq25 y \geq3 2x-y \geq0 x\geq0,y \geq0 Please enter your answer as three numbers, separated by commas in the order p, x, y. If there is no solution, enter no solution.

Minimize $c = 5.45 x + y + 1.5 z + w$ Subject to 5.12x-y+w \geq1,500 z+w \geq1,500 1.12x+y \leq1,000 x\geq0,y\geq0,z \geq0

Solve the standard minimization problem using duality. Minimize $c = 5 s + 4 t$ subject to 3s+t\geq30 s+t\geq20 s+3t\geq30 s\geq0,t\geq0 $c =$ $s =$ $t =$ ___

Solve the games with the given payoff matrix. $P = \left[ \begin{array} { l l l } - 3 & - 5 & - 2 \\- 3 & - 2 & - 4 \\- 4 & - 3 & - 3\end{array} \right]$

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

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Exam 6: Linear Programming

Maximize p=2x+3y+1.1z+4wp = 2 x + 3 y + 1.1 z + 4 wp=2x+3y+1.1z+4w Subject to 1.2x+y+z+w \leq42 2.2x+y-z-w \geq15 1.2x+y+z+1.2w \geq11.5 x\geq0,y\geq0,z\geq0,w \geq0 Round all answers to two decimal places.

Minimize c=5x+8yc = 5 x + 8 yc=5x+8y subject to the following (using the simplex method). ​ 7x+3y\geq30 2x+3y\geq12 x\geq0,y\geq0 ​ c=c =c= __________ ​ x=x =x= __________ ​ y=y =y= __________

Which system does the graph satisfy

Solve the linear programming problem. Minimize C=−3x−5yC = - 3 x - 5 yC=−3x−5y subject to 2x+3y\leq12 7x-6y\leq30 x\geq0,y\geq0 ​ x=x =x= __________ y=y =y= __________ C=C =C= __________

Maximize p=x+2yp = x + 2 yp=x+2y Subject to x+y \leq20 y \geq8 2x-y \geq0 x\geq0,y \geq0

Solve the standard minimization problem using duality. 3s+2t+u\geq150 2s+t+3u\geq150 subject to s+3t+2u\geq150 s\geq0,t\geq0,u\geq0 If you have several solutions, select one of them.

Maximize ​ p=x+2yp = x + 2 yp=x+2y ​ subject to ​ x+y \leq25 y \geq3 2x-y \geq0 x\geq0,y \geq0 ​ Please enter your answer as three numbers, separated by commas in the order p, x, y. If there is no solution, enter no solution.

Minimize c=5.45x+y+1.5z+wc = 5.45 x + y + 1.5 z + wc=5.45x+y+1.5z+w Subject to 5.12x-y+w \geq1,500 z+w \geq1,500 1.12x+y \leq1,000 x\geq0,y\geq0,z \geq0

Solve the standard minimization problem using duality. ​ Minimize c=5s+4tc = 5 s + 4 tc=5s+4t ​ subject to 3s+t\geq30 s+t\geq20 s+3t\geq30 s\geq0,t\geq0 ​ c=c =c= __________ ​ s=s =s= __________ ​ t=t =t= ___________

Solve the games with the given payoff matrix. P=[−3−5−2−3−2−4−4−3−3]P = \left[ \begin{array} { l l l } - 3 & - 5 & - 2 \\- 3 & - 2 & - 4 \\- 4 & - 3 & - 3\end{array} \right]P=​−3−3−4​−5−2−3​−2−4−3​​

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 $p = 2 x + 3 y + 1.1 z + 4 w$ Subject to 1.2x+y+z+w \leq42 2.2x+y-z-w \geq15 1.2x+y+z+1.2w \geq11.5 x\geq0,y\geq0,z\geq0,w \geq0 Round all answers to two decimal places.

Minimize $c = 5 x + 8 y$ subject to the following (using the simplex method). 7x+3y\geq30 2x+3y\geq12 x\geq0,y\geq0 $c =$ $x =$ $y =$ __

Solve the linear programming problem. Minimize $C = - 3 x - 5 y$ subject to 2x+3y\leq12 7x-6y\leq30 x\geq0,y\geq0 $x =$ $y =$ $C =$ __

Maximize $p = x + 2 y$ Subject to x+y \leq20 y \geq8 2x-y \geq0 x\geq0,y \geq0

Maximize $p = x + 2 y$ subject to x+y \leq25 y \geq3 2x-y \geq0 x\geq0,y \geq0 Please enter your answer as three numbers, separated by commas in the order p, x, y. If there is no solution, enter no solution.

Minimize $c = 5.45 x + y + 1.5 z + w$ Subject to 5.12x-y+w \geq1,500 z+w \geq1,500 1.12x+y \leq1,000 x\geq0,y\geq0,z \geq0

Solve the standard minimization problem using duality. Minimize $c = 5 s + 4 t$ subject to 3s+t\geq30 s+t\geq20 s+3t\geq30 s\geq0,t\geq0 $c =$ $s =$ $t =$ ___

Solve the games with the given payoff matrix. $P = \left[ \begin{array} { l l l } - 3 & - 5 & - 2 \\- 3 & - 2 & - 4 \\- 4 & - 3 & - 3\end{array} \right]$