**Assignment Instructions for Submission**Submit solutions to the following problems in a single PDF document, preferably completed using LaTeX. It is likely that you will need to use programming (Python) or a matrix calculator to solve most of the problems. You do not need to submit the code, but you should include explanations of all your conclusions.**Problem Statement**2. (Tucker, 1993) A furniture manufacturer makes tables, chairs, and sofas. In one month, the company has available 300 units of wood, 350 units of labor, and 225 units of upholstery. The manufacturer wants a production schedule for the month that uses all these resources. The various products require the following amounts of the resources.| | Table | Chair | Sofa ||----------------|-------|-------|------|| **Wood** | 4 | 1 | 3 || **Labor** | 3 | 2 | 5 || **Upholstery** | 2 | 0 | 4 |a. Set up and solve a system of equations to determine how much of each product should be manufactured.b. Suppose there is an error in the upholstery requirements. The table needs 0 units and the chair needs 2 units. How does this change the production schedule?c. Suppose in one month the company has 310 units of wood, 345 units of labor, and 230 units of upholstery. How does this change the production schedule?

Given that a furniture manufacturer makes table, chairs and sofas.In a month, the company has…

Answered: (Tucker, 1993) A furniture manufacturer…

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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farmer maggot bought 40 bushels of wheat, 24 bushels of barley, and 20 bushels of oats for $354.85. Mr. Jones bought 26 bushels of wheat, 30 bushels of barley and 50 bushels of oats for $403.90. Old MacDonald bought 24 bushels of wheat, 120 bushels of barley and 100 bushels of oats for $956.73. a. develop a system of linear equations based on this scenario b. translate that system of linear equations into an augmented matrix and solve it c. what did the famrers pay for these commondidites? in addition to showing the calculations that lead to your solution, write a synopsis of the tactic (s) you used to arrive at your solution to this question. Use clear and concise vocabulary sentence structure and grammer. Your answer should be labled with approriate units and reflec the context used in this question
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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
4. Students were asked to formulate the system of equations needed to solve the following problem: One serving of Pork & Beans contains 5 grams of protein and 21 grams of carbohydrates. A typical slice of white bread provides 2 grams of protein and 11 grams of carbohydrates. George is planning a meal of beans on toast and wishes to have it supply 30 grams of protein and 139 grams of carbohydrates, respectively. Determine the amount of beans and the amount of bread George should include in his meal. Several students wrote the following and it was marked incorrect: Let x amount of protein y = amount of carbohydrates 5x+21y = 30 2x+11y = 139 Cross out the mistakes and make corrections. You do not need to solve the system of equations.
1. Define the variables, write a system of equations, solve, and then write the answer in a sentence. Sarah is the director of the marching band, and she must order 35 new uniforms for all of the boys and girls in the band. There are usually five more girls than twice the number of boys in the band. How many uniforms of each type should she order?
You have three types of ground coffee: cheap ($5/pound), medium ($8/pound), and expensive Arabica ($14/pound). You want to make a blend that costs $10/pound, and you want to make 50 pounds of it. You also want to be able to say "contains 20% Arabica" without lying. Set up and solve a linear system to find out how much of each type of coffee you should use, while spending the least money.

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