A factory is producing three different type of product X, Y and Z. Each unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1 hours of labor respectively. Each unit of product X, Y and Z requires 1 hour of Machine, (-2) hour of Machine and 5 hours of Machine respectively. Each unit of product X, Y and Z requires 10kg of material, 5kg of material and 4kg of material respectively. Factory has maximum 100 hours of labor, 80 hours of Machine and 300 Kg of Material. What combination of three type of product produce that maximize profit with in a given constraints, if per unit profit on product X is Rs.2, per unit profit on product Y is Rs.12 and per unit profit on product Z is Rs.8. i. Find the solution using simplex method of linear programming. Interpret the initial table. Why slack variable is added in structural constraints? Interpret the meaning of slack variable if X = Y = Z = 15 units ii. i.

A factory is producing three different type of product X, Y and Z. Each unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1 hours of labor respectively. Each unit of product X, Y and Z requires 1 hour of Machine, (-2) hour of Machine and 5 hours of Machine respectively. Each unit of product X, Y and Z requires 10kg of material, 5kg of material and 4kg of material respectively. Factory has maximum 100 hours of labor, 80 hours of Machine and 300 Kg of Material. What combination of three type of product produce that maximize profit with in a given constraints, if per unit profit on product X is Rs.2, per unit profit on product Y is Rs.12 and per unit profit on product Z is Rs.8. i. Find the solution using simplex method of linear programming. Interpret the initial table. Why slack variable is added in structural constraints? Interpret the meaning of slack variable if X = Y = Z = 15 units ii. i.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Indahkiat has a daily budget of 320 hours of labor and 350 units of raw material manufacture two…

A: Given, Given, The model is Max z= 10x1+12x2-2x3subject to x1+2x2-x3≤320…

Q: A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota…

A: Given, Fixed cost=$66240 Variable cost per unit=$(202+12x) Selling price per unit=$(1194-12x) Where…

Q: A company manufactures x units of Product A and y units of Product 8, on two machines, I and II. The…

Q: Example 2. A pharmaceutical company manufactures three type of medicines A, B and C. The processing…

Q: Units of Product A and y units of Product B, on two machines, I and II. It has been determined that…

A: let's consider the constraints on the values for x and y: x≥0 and y≥0 since product produced can…

Q: A company produces two products: A and B. The profit per unit of product A is 4, and the profit per…

A: The profit per unit of product A = 4The profit per unit of product B = 5For product A,the production…

Q: Laminated core, windings and insulating material are three basic parts of component to create a…

Q: units of special lamp and the regular lamp should be produced per production period in order to…

Q: A refinery has two smelters that extract metallic iron ore. Smelter A pro- cesses 1000 tons of iron…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: 2 2) A factory makes three types of granola cereal: Plain, Nutty, and Chewy. Each batch of Plain…

A: Let us consider the system of equation AX=b Now, the solution of the system using the cramer's rule…

Q: A farmer can plant either rice or squash on his land. Each rice plant requires three square meters…

A: Let x represents the rice and y represents the squash. From the given information, the land…

Q: The constraints and the objectives that are used to "reduce the amount of overtime for both machines…

Q: Smurfs Ice Cream produces three types of ice cream by using sugar, milk, and flavor: Smurfette…

A: Given flavors of ice creams are, Smurfette, Gargamel and Jockey. Cost of sugar per Kg =x Cost of…

Q: A company produces three types of bicycles, i.e., mountain bike, road bike, and touring bike... For…

A: Let there are x mountain bikes there are y road bikes There are z touring bikes For the given data…

Q: A company manufactures two products: X and Y, Product X costs $8 per unit and contains 2 units of…

A: We have two product X and Y, Product X costs $8 per unit and contains 2 units of raw material 1, 6…

Q: A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero…

A: As per the question a dietician is creating a snack package that must meet certain nutritional…

Q: If ten components are to be stacked into a cylindrical casing. Component 1 and 2 need to be at the…

A: Given three components are of one type and identical to one another and two components areof…

Q: A paper tissue factory produces three models (I,II,III) of tissues using two types of raw materials…

A: Requirement of each type of the three modelRaw materialIIIIIIAvailability of each type of raw…

Q: For the management of rice root nematodes carbofuran 3G @ 1 kg a.i./ ha is recommended and the cost…

A: To work out the total cost of nematode management using carbofuran 3G, we need to consider the…

Q: A bicycle manufacturer makes mountain bikes and road bikes. Each mountain bike requires 2 units of…

Q: Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Average 31 35.5 31 40.5 34 39 37.5 time for Total process…

A: Correlation The correlation is a statistical technique that is used for analyzing the behavior and…

Q: tables and chests. Producing a chair requires 2 hours of construction and 1 hour of painting.…

Q: A produce grower is purchasing fertilizer containing 3 nutrients: A, B and C. The minimum weekly…

A: (a) Write down the LP Model. In Blend 1,the number of units of the nutrient of A is 2n .In Blend…

Q: A furniture maker makes three different style of wardrobes: x, x, and x,. The manufacture of each…

A: Given: A furniture maker makes three different styles of wardrobes: x1, x2, and x3. The manufacture…

Q: A company has three machines B1, B2 and B3for making 1kN resistors. It has been observed that 70% of…

Q: Happy Kid Toy Company produces two types of toy cars, A and B. The company makes RM 50 profit for…

Q: Protective Research, Inc. received an order to produce a specially designed fence for preventing…

A: We will construct a linear programming problem according to the given conditions and solve it using…

Question

A factory is producing three different type of product X, Y and Z. Each
unit of product X, Y and Z requires 2 hour of labor, 2 hours of labor and 1
hours of labor respectively. Each unit of product X, Y and Z requires 1
hour of Machine, (-2) hour of Machine and 5 hours of Machine
respectively. Each unit of product X, Y and Z requires 10kg of material,
5kg of material and 4kg of material respectively. Factory has maximum
100 hours of labor, 80 hours of Machine and 300 Kg of Material. What
combination of three type of product produce that maximize profit with in
a given constraints, if per unit profit on product X is Rs.2, per unit profit
on product Y is Rs.12 and per unit profit on product Z is Rs.8.
i.
Find the solution using simplex method of linear programming.
Interpret the initial table.
Why slack variable is added in structural constraints? Interpret
the meaning of slack variable if X = Y = Z = 15 units
ii.
i.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Factorization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

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 company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company’s resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufacturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit.a) Formulate a linear programming model for this problem.
A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the boors, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost por unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery noeds at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package. a. Write a system of inequalities to express the conditions of the problem. b. Graph the feasible region of the system. a. Fill in the chart. Protein Carbohydrates Fat Fruit unit(s) per ounce unit(s) per ounce unit(s) per ounce Nuts unit(s) per ounce unit(s) per ounce unit(s) per ounce .. Requirements per package At least At least No more than unit(s) unit(s) unit(s)
A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 6 units of protein 4 units of carbohydrates, and 4 unit of fat, and will contain 18 calories. Each K ounce of nuts will supply 3 units of protein, 3 unit of carbohydrate, and 5 units of fat, and will contain 29 calories. Every package must provide at least 6 units of protein, at least 10 units of carbohydrates, and no more than 11 units of fat. What is the least number of calories possible in a package? Write out the inequality for protein using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) Write out the inequality for carbohydrates using x and y as your variables for ounces of fruit and nuts respectively (Use variables in order) 0 Write out the inequality for fat using x and y as your variables for ounces of fruita my instructor srespectively (Use variables in order)
A company uses four special tank trucks to deliver four different gasoline products to customers. Eachtank has five compartments with capacities: 500, 750, 1200, 1500, and 1750 gallons. The daily demands forthe four products are 10000, 15000, 12000, and 8000 gallons. Any quantities that cannot be delivered by thecompany’s four trucks must be subcontracted at the additional costs of 5, 12, 8, and 10 cents per gallon forproducts 1, 2, 3, and 4, respectively. The goal is to develop the optimal daily loading schedule for the fourtrucks that will minimize the additional cost of subcontracting. Formulate this problem as an integer linearprogram, and solve it using linear program solver.
XYZ Corporation operates two plants, each of which has a capacity of 200 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 17 units per day while customer D has a demand of 349 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 25 19 12 14 Plant 2 15 21 23 20 How many units should XYZ ship from each plant to each customer?