Q1: There is a factory working to produce two pump types (X, Y), by using fourparts ( A, B, C, and D).Product XProduct Y1-To make one pump of product X we need: 9 parts of A, 6 parts of B, and 8parts of C.2-But to make one pump of product Y we need : 6 parts of A, 12 parts of B,5 parts of C, and 2 parts of D.The factory tries to sell a large number ofeach product . The profit of onepiece of product X S300 and $250 for Y. If you know there are only 540parts available of A, 720 parts of B, 400 parts of C, and 100 ofD.1- Create the table, and formulate the problem as a linear program.2- Solve the problem to find, which must produce sell.

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Answered: Q1: There is a factory working to…

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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Q1) A company manufactures two products (pl and p2) on three machines (ml, m2 and m3). Each of the products must be processed on all three machines. One unit of pl requires 5h (hours) of processing time on ml, 4h of processing time on m2 and 3h processing time on m3. Machining times required by a unit production of p2 are 2h, 3h and 4h respectively. The machine capacities are 270h, 250h, and 200h per pieces respectively. The unit profits for the products are $100 and $60 respectively. Additionally the manufacturer wants to produce at least five pl for each p2. Suppose that the produced each product is sold. Formulate a Linear Programming (LP) Model to determine the number of pl and p2 that maximize the overall profit. (Define the decision variables. Write the objective function, and the constraints. Indicate sign restrictions. Do not try to solve the problem.)
A manufacturer produces three products: Product A, Product B and Product C. Tobe able to produce each product he uses a combination of three distinct inputsnamely Input I, Input II and Input III the supply of which is currently at 730, 350and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3units of Input II and 4 units of Input III to be produced. Similarly, each unit ofProduct B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5units of Input I, 1 unit of Input II and 3 units of Input III.(i) Let a, b and c represent the number of units produced of Products A, B and Crespectively. The manufacturer must decide what quantity of each product toproduce so that his entire supply of inputs is utilized. Formulate his/herdecision in the form of a system of three linear equations in the variables a, band c. [3 marks](ii) Rewrite the above system of linear equations in the matrix form Ax = b. [2 marks](iii) Hence or otherwise, determine how…
Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁1 dt dx1 dt pure water 3 gal/min mixture 4 gal/min This system is described by the system of equations 1 50 2 25 dx2 dt 2 25 2 25*1 1 + -X2 mixture 1 gal/min -X2 B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 3 pounds of salt per gallon is pumped into tank A? -2 25*1 + 50x2+6× dx2 2 - (25)*₁- (25)×₂2 - = x2 dt…
This is System Modeling & Simulation question
Turbo Coolers Inc. builds cooling systems for industrial plants. A Type A cooler takes 80 W of power and can cool 18 liters of fluid per minute under the given conditions. A Type B cooler takes 100 W of power and can cool 60 liters of fluid per minute. A Type A cooler costs $3,500 and a Type B cooler costs $12,000. The factory has up to 1,000 W of power it can supply for cooling, and must cool 300 liters of fluid per minute. How many of each type of cooler should Turbo Coolers Inc. install in the factory to minimize cost? Formulate a linear programming model for this situation. Solve this model using graphical analysis. Display your graph and the solution parameters. Create your graph using Microsoft Word or Excel and submit it to your instructor. Create your graph using Microsoft Word or Excel and submit it to your instructor.
A drug company manufactures two kinds of sleeping pill: Pill 1 and Pill 2. The pills contain a mixture of two different chemicals, A and B (and no other ingredients). Pill 1 must contain at least 65% Chemical A and Pill 2 must contain at least 55% Chemical A. There are two different ways to produce Chemicals A and B. Operating Process P requires 7 Kgs of A raw material to run for one hour and 2 hours of labor time (because it must be supervised by 2 workers). Operating Process Q requires 5 Kgs of A raw material to run for one hour and 3 hours of labor time. Operating Process P produces three Kgs of each chemical for one hour runtime. Operating Process Q produces 3 Kgs of Chemical A and one Kg of Chemical B for one hour runtime. There are L > 0 hours of labor and R > 0 Kgs of raw material available. The company earns A profit from Pill i of πi ≥ 0 (i = 1,2) Kshs per Kg. The company wishes to find a production plan that maximizes the profit it makes from manufacturing sleeping…
x = 7v2u+7w, y = 2u - 9v – 3w, and z = 7v5u - 10w implies a(x, y, z) d(u, v, w) =
Q4 Write on paper for upvote and Provide Exact value please.
Find the weight of dried fruit contained within the cakes sent to cake shops P and Q that results from 450 kg of dried fruit distributed from wholesaler A and 750 kg of dried fruit distributed from wholesaler B. If 450 kg of dried fruit was distributed from wholesaler A to bakeries X,Y and Z and 750 kg of dried fruit was distributed from wholesaler B to bakeries X,Y and Z, how much fruit were in the cakes received in cakes by cake shops P and Q.
A manufacturer produces three products; Product A, Product B and Product C. To be able to produce each product he uses a combination of three distinct inputs namely Input I, Input II, and Input III the supply of which is currently at 300, 545 and 430 units, respectively. Each unit of Product A requires 2 units of Input I, 5 units of Input II and 1 unit of Input III to be produced. Similarly, each unit of Product B requires 3 units of Input 1 and 3 units of Input II while Product C uses 1 unit of Input I, 2 units of Input II and 4 units of Input III. How many units of each product can be produced? Hi again, This is another matrixes question and still getting problems with them
C and D

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