Formulate but do not solve the following exercise as a linear programming problem.Beyer Pharmaceutical produces three kinds of cold formulas: x thousand bottles of Formula I, y thousand bottles Formula II, and z thousand bottles Formula III. It takes 1.5 hr to produce 1,000 bottles ofFormula I, 3 hr to produce 1,000 bottles of Formula II, and 4.5 hr to produce 1,000 bottles of Formula III. The profits for each 1,000 bottles of Formula I, Formula II, and Formula III are $170, $220, and$300, respectively. For a certain production run, there are enough ingredients on hand to make at most 13,000 bottles of Formula I, 10,000 bottles of Formula II, and 14,000 bottles of Formula III.Furthermore, the time for the production run is limited to a maximum of 60 hr. How many bottles of each formula should be produced in this production run so that the profit, P (in dollars), is maximized?Maximizeproduction timeFormula IFormula IIFormula IIIP =x ≥ 0y ≥ 0Z≥ 0subject to the constraints

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Answered: Formulate but do not solve 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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Solve the following linear programming problem. You are taking two dietary supplements daily: Supplement A and Supplement B. An ounce of supplement A contains 9 units of calcium, 8 units of vitamin D, and 5 units of sodium. An ounce of supplement B contains 2 units of calcium, 4 units of vitamin D, and 3 units of sodium. Your goal is to get at least 90 units of calcium and at least 120 units of vitamin D from the supplements daily, while at the same time reducing the amount of sodium that you will get. How many ounces of each supplement should you take daily to reach your goals? Ounces of Supplement A =  Blank 1. Fill in the blank, read surrounding text. Ounces of Supplement B =  Blank 2. Fill in the blank, read surrounding text. How many units of sodium will you get daily under these circumstances? Units of Sodium =  Blank 3. Fill in the blank, read surrounding text.
Formulate but do not solve the problem.The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $44 and $28 per acre, respectively. Jacob Johnson has $17,200 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? (Let x and y denote the number of acres of corn and wheat, respectively.)   = 500   = 17,200
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P =      subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Just make the linear programming model of the next exercise: A company manufactures and sells two lamp models L1 and L2. For its manufacture, a manual work of 30 minutes is needed for the L1 model and 45 minutes for the L2, and a machine work of 25 minutes for L1 and 15 minutes for L2. 150 hours per month are available for manual work and 120 hours per month for the machine. Knowing that profit per unit is $150 and $100 for L1 and L2 respectively, plan production to maximize profit. Please be as clear as possible and show all the steps. Thank you very much
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0

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