Product Blend ExamplePetroleum Mix InputsComponent123Petroleum Mix ProductsComponentSpecificationsGradeSuperPremiumMaximum BarrelsAvailable/Day4,5002,7003,500ExtraAt least 50% of 1Not more than 30% of 2At least 40% of 1Not more than 25% of 3At least 60% of 1At least 10% of 2Cost/Barrel$121014SellingPrice/Barrel$232018• Produce at least 3,000 Barrels of each grade. Looking back at the Product Blend Example, what would the constraint look like if you needed atleast 45% of "Super" Grade to be Component #2?Remember, xij = barrels of component i used in motor oil grade j per day,where i = 1, 2, 3 and j = s (super), p (premium), and e (extra).So, X1e is the number of barrels of Component #1 used in the Extra grade oil, per day.0.45x25 -0.55x15 - 0.55x35 ² 0.00.7x1e - 0.3x2e - 0.3x3e ≥ 0.00.55x2s - 0.45x15 -0.45x35 ≤ 0.450.55x25 -0.45x15 -0.45X35 ²0.0

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Answered: Product Blend Example • Petroleum Mix…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 81E

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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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Product Blend Example • Petroleum Mix Inputs Maximum Barrels Available/Day 4,500 2,700 3,500 Petroleum Mix Products Component 1 2 3 Cost/Barrel $12 10 14