A dietitian in a hospital is to arrange a special dietcomposed of three basic foods. The diet is toinclude exactly 340 units of calcium, 180 units ofiron, and 400 units of vitamin A The number of unitsper ounce of each special ingredient for each of thefoods is indicated in the table. Construct aUnits per OunceFood AFood BFood CCalcium301020Iron101020Vitamin Amathematical model to complete parts (A) through(C) below. Use Gauss-Jordan elimination to solvethe model and then interpret the solution.3030Construct a mathematical model for this situation. Let the first, second, and third equations represent calcium, iron, and vitamin A, respectively. Let x, represent thenumber of ounces of food A, x, represent tine number of ounces of food B, and x, represent the number of ounces of food C.- 2 * 3 =X, +X, +%3D(Type integers or decimais.)20

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Answered: A dietitian in a hospital is to arrange…

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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A circuit has four resistors and two voltage sources. The resistors are R1= 0.001, R₂ = 3.33, R3 = 4, and R4 = 0.012 ohms; the voltage sources are E₁ = 12 and E₂ = 10 volts; and the current are 1₁, 12, and i3 amps. By using Kirchohoff's laws, we have the linear system 0.0131, +3.331₂ 0.013/₁ 1₁ 1₂ = 22 + 413 = 12 13 = 0 (a) Use Gaussian elimination without pivoting and three-digit rounding to solve the system. (b) Use Gaussian elimination with partial pivoting and three-digit rounding to solve the system. (c) Use Gaussian elimination with complete pivoting and three-digit rounding to solve the system.
The following linear system is in echelon form. Solve the linear system by back substitution. ×₁-5x2+x3 = 18 X2+x3 = 8 ... What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. There is a unique solution, X₁ = 1×2 = (Type integers or simplified fractions.) X3 = B. There are infinitely many solutions of the form x₁ = t is a real number. ' 1×2 = ,X3=t, where (Simplify your answers. Use integers or fractions for any numbers in the expressions.) C. There are infinitely many solutions of the form x₁ = and t are real numbers. X2S, x3 =t, where s (Simplify your answers. Use integers or fractions for any numbers in the expressions.) D. There is no solution.
Set up a system of equations and then solve using Gauss-Jordan elimination.A manufacturer of portable tools has three sets, Basic, Homeowner, and Pro, which must be painted, assembled, and packaged for shipping. The following table gives the number of hours required for each operation for each set. Basic Homeowner Pro Painting 1.6 1.9 3 Assembly 0.5 1.3 1.9 Packaging 0.5 0.5 1.7 If the manufacturer has 91.3 hours for painting per day, 50.1 hours for assembly per day, and 31.9 hours for packaging per day. How many sets of each type can be produced each day?The manufacturer can produce Basic sets, Homeowner sets and Pro sets per day.
Solve the following system of linear equations. If there is no solution, write DNE. If there are multiple solutions, use x1, x2, or x3 as your free variable(s) as appropriate. xi + x2 + 5x3 : 1 x2 + 2x3 - 7 %3D 0 = – 4 X2 = X3 =
Statistics show that at a certain university, 90% of the students who live on campus during a given semester will remain on campus the following semester, and 70% of students living off campus during a given semester will remain off campus the following semester. Let x and y denote the number of students who live on and off campus this semester, and let u and v be the corresponding numbers for the next semester. Then the following system of equations can be formed. Complete parts a through c. .9x +.3y = u .1x .7y = v (a) Write this system of equations in matrix form. (b) Solve the resulting matrix equation for X= x y (c) Suppose that, out of a group of 42,000 students, 24,000 currently live on campus and 18,000 live off campus. How many lived on campus last semester? How many will live off campus next semester?
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless ___ dozen short-sleeve ___ dozen long-sleeve ___dozen
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless ___ dozen short-sleeve ___dozen long-sleeve ___ dozen
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 9x1 + 29x2 + X3 = 15 4x, + 13x2 + 2x3 = -7 X, + 3x2 - 3x3 = 5 Select the correct choice below and, if necessary, fillin the answer box(es) to complete your choice. A. The unique solution is X, =, X2 = and X3 = B. The system has infinitely many solutions. The solution is x, = ,X2 = and x, =t. (Simplify your answer. Type an expression using t as the variable.) C. The system has infinitely many solutions. The solution is x, = , X2 =s, and x, =t. (Simplify your answer. Type an expression using s and t as the variables.) D. There is no solution.

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