Bob, a nutritionist who works for the University Medical Center, has been asked to prepare special diets for two patients, Susan and Tom. Bob has decided that Susan's meals should contain at least 400 mg of calcium, 20 mg of iron, and 54 mg of vitaminC, whereas Tom's meals should contain at least 360 mg of calcium, 16 mg of iron, and 46 mg of vitamin C. Bob has also decided that the meals are to be prepared from three basic foods: Food A, Food B, and Food C. The special nutritional contents ofthese foods are summarized in the accompanying table. Find how many ounces of each type of food should be used in a meal so that the minimum requirements of calcium, iron, and vitamin C are met for each patient's meals.Susan's meals:Food AFood BFood CTom's meals:Food AFood BFood CNeed Help?Food AFood BFood COZOZOZOZOZOzRead ItContents (mg/oz)Calcium302520Iron Vitamin C1Watch It12254

Given that Susan's meals should contain at least 400 mg of calcium, 20 mg of iron, and 54 mg of…

Answered: Bob, a nutritionist who works for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 70 students, requires 5 chaperones, and costs $1,400 to rent. Each van can transport 10 students, requires 1 chaperone, and costs $90 to rent. Since there are 700 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 700 students. Since only 60 parents have volunteered to serve as chaperones, the officers must plan to use at most 60 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs? The officers should rent buses and vans to minimize the transportation costs.
Mandrake Falls High School is losing a lot of money through its school laboratories. Accidents and misuse of equipment by students are taking their toll on laboratory supplies. In an attempt to remedy this, Mandrake is experimenting with a weekend course in laboratory techniques. For the time being, lack of resources allow only a portion of Mandrake's lab students to take the weekend course: of the 200 students enrolled in lab classes at Mandrake, only 75 have been able to take the weekend course. Mandrake is interested in evaluating the course's effectiveness in propagating safety in the laboratories. During regular lab classes, lab instructors are recording harmful lab incidents: accidents, misuse of lab equipment, etc. The high school is looking at the data and examining two variables: laboratory performance ("involved in no incident", "involved in exactly one incident", or "involved in 2+ incidents") and status regarding lab techniques course ("took the techniques course" or…
You would like to make a nutritious meal of eggs, edamame, and elbow macaroni. The meal should provide at least 30 g of carbohydrates, at least 20 g of protein, and no more than 60 g of fat. An egg contains 2 g of carbohydrates, 17 g of protein, and 14 g of f A serving of edamame contains 12 g of carbohydrates, 12 g of protein, and 6 g of fat. A serving of elbow macaroni contains 43 g of carbohydrates, 8 g of protein, and 1 g of fat. An egg costs $2, a serving of edamame costs $5, and a serving of elbow macaroni costs $3. Formulate a linear optimization model that could be used to determine the number of servings of egg, edamame, and elbow macaroni that should be in the meal in order to meet the nutrition requirements at the minimal cost. a) Define the decision variables. b) Write down the objective function. c) Write down the constraints.type solution pls
Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish—chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible amounts of bell peppers and spices. A jar of chow-chow contains 8 ounces of cabbage, 3 ounces of tomatoes, and 3 ounces of onions, whereas a jar of tomato relish contains 6 ounces of tomatoes, 6 ounces of cabbage, and 2 ounces of onions. The Rays grow 120 pounds of cabbage, 90 pounds of tomatoes, and 45 pounds of onions each summer. The Rays can produce no more than 24 dozen jars of relish. They make $2.25 in profit from a jar of chow-chow and $1.95 in profit from a jar of tomato relish. The Rays want to know how many jars of each kind of relish to produce to generate the most profit.a. Formulate a linear programming model for this problem. b. Solve this model graphically. c. Solve this model…
A patient takes vitamin pills. Each day he must have at least 300IU of vitamin A, 3 mg of vitamin B1, and 60 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 1 mg of vitamin B1, and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 1 mg of vitamin B1, and 40 mg of vitamin C. Pill 1 costs 25¢, and pill 2 costs 50¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy nothing of pill 1 and nothing of pill 2. The minimum cost is $ nothing. (Simplify your answers. Type integers or decimals.)
Hello Dolly, Inc. crafts three styles of dolls: Lexi, Maysy, and Dizzy. Each doll requires sewing time, painting time, and supplies. Sewing machines are available for only 118 hours, only 2805 hours are available for painting, and 390.5 lbs. of supplies are available. Each Lexi doll requires 0.2 hours of sewing, 9 hours of painting, and 0.7 lbs. of supplies. Each Maysy doll requires 0.4 hours of sewing, 10 hours of painting, and uses 0.9 pounds of supplies. Each Dizzy doll requires 0.5 hours of sewing, 7 hours of painting, and 2 pounds of supplies. If the company earns a profit of $145 per Lexi doll, $155 per Maysy doll, and $150 per Dizzy doll, how many of each doll should the company produce to maximize profit? How much profit will result? (Use for the number of Lexi dolls, y for the number of Maysy dolls, and z for the number of Dizzy dolls.) Maximize P = subject to ≤118 ≤2805 <390.5 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes…
For his classes, Professor Wright gives three types of quizzes, objective, recall, and recall-plus. To keep his students on their toes, he has decided to give at least 20 quizzes next quarter. The three types, objective, recall, and recall-plus quizzes, require the students to spend, respectively, 10 minutes, 30 minutes, and 60 minutes for preparation, and Professor Wright would like them to spend at least 12 hours(720 minutes) preparing for these quizzes above and beyond the normal study time. An average score on an objective quiz is 5, on a recall type 6, and on a recall-plus 7, and Dr. Wright would like the students to score at least 130 points on all quizzes. It takes the professor one minute to grade an objective quiz, 2 minutes to grade a recall type quiz, and 3 minutes to grade a recall-plus quiz. How many of each type should he give in order to minimize his grading time?
A vendor specializing in outdoor gear offers customers three ways to place orders for home delivery. Customers can place orders either in the store, online, or via telephone using a catalog. Of the orders, three-quarters are made online with one-eighth each made in stores or via telephone. Of the online orders, 30% are only for clothing, 30% are only for camping supplies, and 40% are for both. For orders placed in the store, all are for clothing (to order a size that is not in stock). Among orders placed via telephone, 50% are only for clothing, 20% are only for camping supplies, and 30% are for both. Answer parts (a) and (b). (a) Organize these probabilities as a probability table. Purchase Method On-Line In Store Telephone Total Clothing 0.225 0.125 0.0625 0.4125 Purchase Camping 0.225 0.025 0.25 Both 0.3 0. 0.0375 0.3375 Total 0.75 0.125 0.125 1 (Simplify your answers. Type integers or decimals.) (b) What's the probability that the customer orders clothing, either by itself or in…
The Cheery Cherry Chair Company makes three types of chairs, the Montegue, the Capulet, and the Verona. Each chair requires assembly, finishing, and a certain amount of wood to make. The assembly area can be used for at most 10 hours per day. To keep him busy, the finishing person needs to work at least 6 hours per day. Producing a Montegue requires 1 hour of assembly, 2 hour of finishing, and 9 board feet of wood. Producing a Capulet requires 1 hour of assembly, 1 hour of finishing, and 9 board feet of wood. Finally, producing a Verona requires 2 hour of assembly, 1 hour of finishing, and 3 board feet of wood. If the company wants to minimize the amount of cherry wood used, how many should they make of each model? (It is possible to complete a fractional part a chair in a given day; in the long run you end up with completed chairs.) Number of Montegues = Number of Capulets = Number of Veronas = How many board feet of cherry wood would be used each day?
The Southfork Feed Company makes a feed mix from four ingredients--oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements for the mix:• At least 30% of the mix must be soybeans. • At least 20% of the mix must be the vitamin supplement. e The ratio of corn to oats cannot exceed 2 to 1. •The amount of oats cannot exceed theamount of soybeans. • The mix must be atleast 500 pounds.A pound of oats costs $0.50, a pound of corn, $1.20, a pound of soybeans, $0.60, and a pound of vitamin supplement, $2.00. The feed company wants to know the number of pounds of each ingredient to put in the mix to minimize cost. a. Express constraint of at least 30% of the mix must be soybeans b. Express constraint of at least 20% of the mix must be the vitamin supplement c. Express Constraint of the ratio of corns to oats cannot exceed 2…

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