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An entrepreneur decided to set up a soda business. Due to this intention he bought a PET bottle filling line. According to manufacturer's data, this line has to be operated by 4 workers. The manufacture is working in two-shifts with 7.75 working hours per shift. Annual there are 252 working days. In average there are annually 15 days of vacation, 5 days of sickness, and 2 day of other absence. The expected time loss due to operation is 72 hours. 1. How many workers have to be hired to ensure a smooth operation? The answer is [MPN]

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 22EQ

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Calculate manpower need
An entrepreneur decided to set up a soda business. Due to this intention he bought a PET bottle
filling line. According to manufacturer's data, this line has to be operated by 4 workers. The
manufacture is working in two-shifts with 7.75 working hours per shift. Annual there are 252 working
days. In average there are annually 15 days of vacation, 5 days of sickness, and 2 day of other
absence. The expected time loss due to operation is 72 hours.
1. How many workers have to be hired to ensure a smooth operation? The answer is [MPN]

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Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.

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