how to do? A cereal manufacturer wishes to produce 1000 pounds of a cereal that contains exactly 10% fiber,2% fat, and 5% sugar (by weight). The cereal is to be produced by combining four items of raw foodmaterial in appropriate proportions. These four items are named A, B, C, D and they have certaincombinations of fiber, fat, and sugar content, and are available at various prices per pound:ItemFiberFatSugarPrice/lbA45132B62644C12951D3802The manufacturer wishes to find the amounts of each item to be used to produce the cereal in theleast expensive way. Formulate the problem as a linear programming problem.

Let,W: amount of item A used,X: amount of item B used,Y: amount of item C used, andY: amount of item…

Answered: A cereal manufacturer wishes to produce…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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A diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. 0.42 X₁ x2 X3 11 34 45 3 0.8 CIES X4 (Type an integer or decimal for each matrix element.) Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Supplied by Diet in One Day a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet. Nutrient Nonfat Soy Whey Milk flour 36 Protein Carbohydrate 52 0 Fat 50 14 33 75 7 1.2 34 45 3
A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?
Zaphod Beeblebrox is mixing drinks that contain three ingredients: Ol' Janx Spirit (ingredient A), water from the seas of Santraginus V (ingredient B) and Arcturan Mega-gin (ingredient C). On his shelf he has three mixtures M1, M2 and M3 containing ingredients A, B and C. The table below is showing the amounts in decilitres of ingredients A, B and C that are contained in 11 of each of the mixtures (11=10dcl). M1 M2 M3 ingredient A 3 ingredient B 3 4 1 ingredient C 5 3 (a) Zaphod made a new mixture using 31 of M1, 21 of M2 and 11 of M3. Determine the amount of each type of ingredient in this mixture. (b) A recipe for Pan Galactic Gargle Blaster requires a mixture that contains 2dcl of ingredient A, 3dcl of ingredient B and 5dcl of ingredient C. Zaphod wants to prepare it using mixtures M1, M2 and M3. What is the minimal and what is the maximal amount of mixture M3 that he can use?
A cereal manufacturer has a machine that fills the boxes. Boxes are labeled "16 ounces," so the company wants to have that much cereal in each box. But no packaging process is perfect, so there will be minor variation. If the weight was set to 16 ounces, then half of the boxes would be underweight, which would not make consumers happy. So, manufacturer sets the weight to 16.3 ounces for filling the boxes. Based on their experience the company knows that the standard deviation will be 0.2 ounces. If the boxes are labled 16 ounces(and expected to weight 16 ounces), then what precentage of the boxes will be underweight? Include a sketch in your answer. Rounding rule for probability: 3 decimal places
Cicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Provide an estimate for the correlation coefficient and interpret the relationship existing between the 13-year cicada’s body weight and wing length.
Cicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Is there a linear relationship between body weight and wing length of 13-year cicadas at 5% level of significance?
Cicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Test whether the wing length of 13-year cicadas is linearly dependent on its body weight at 5% level of significance.
Cicadas are flying, plant-eating insects. One species, the 13-year cicadas (Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada. The adult body weights (BW) in grams and wing lengths (WL) in millimeters are given for three different species of these 13-year cicadas in the following table. It is of interest to determine if body weight is a significant predictor of wing length for a 13-year cicada. Considering all assumptions for a parametric test are satisfied, use the obtained jamovi © outputs below to answer the following: Is it logical to proceed to simple linear regression? If yes, provide an estimate of the simple linear regression line. Specify which variables should be considered as the response and independent variable.
in order to determine which garden fertilizer would work best to increase the growth of radishes you decided to use five different fertilizers on five different radishes. Each of the radishrs were given the sane amount of water and sunlight. what is the independent variabel?
A cable is made up of several parallel strands of wire. The strength of the cable can be estimated from the strengths of the individual wires by either of two methods. In the ductile wire method, the strength of the cable is estimated to be the sum of the strengths of the wires. In the brittle wire method, the strength of the cable is estimated to be the strength of the weakest wire multiplied by the number of wires. A particular cable is composed of 12 wires. Four of them have strength 6000 ± 20 lb, four have strength 5700 ± 30 lb, and four have strength 6200 ± 40 lb. a) Estimate the strength of the cable, and find the uncertainty in the estimate, using the ductile wire method. b) Estimate the strength of the cable, and find the uncertainty in the estimate, using the brittle wire method.
Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroystrees. The researchers will create four different concentrations of fungus mixtures: 0 milliliters per liter (ml/L),1.25 ml/L, 2.5 ml/L, and 3.75 ml/L. An equal number of the insects will be placed into 20 individual containers.The group of insects in each container will be sprayed with one of the four mixtures, and the researchers willrecord the number of insects that are still alive in each container one week after spraying. (a) Identify the treatments, experimental units, and response variable of the experiment.Treatments:Experimental units:Response variable:
Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroystrees. The researchers will create four different concentrations of fungus mixtures: 0 milliliters per liter (ml/L),1.25 ml/L, 2.5 ml/L, and 3.75 ml/L. An equal number of the insects will be placed into 20 individual containers.The group of insects in each container will be sprayed with one of the four mixtures, and the researchers willrecord the number of insects that are still alive in each container one week after spraying. (b) Does the experiment have a control group? Explain your answer.

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