I just need the dual of the problem and an economic interpretation of it ### Linear Programming Problem**Objective Function:**\[ \text{max } z = 3x_1 + 2x_2 \]**Subject to Constraints:**1. $\frac{1}{40} x_1 + \frac{1}{60} x_2 \leq 1$2. $\frac{1}{50} x_1 + \frac{1}{50} x_2 \leq 1$**Non-negativity Constraints:**\[ x_1, x_2 \geq 0 \]**Task:**Find the dual of this example and provide an economic interpretation of the problem.This linear programming problem seeks to maximize the objective function $z$, subject to the given constraints. The variables $x_1$ and $x_2$ must be non-negative. The constraints represent limitations, such as resource or capacity restrictions, and the objective function represents a measure of profit or utility to be maximized. Finding the dual will offer insights into resource valuation and trade-offs.

Name: I just need the dual of the problem and an economic interpretation of
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: I just need the dual of the problem and an economic interpretation of it ### Linear Programming Problem**Objective Function:**\[ \text{max } z = 3x_1 + 2x_2 \]**Subject to Constraints:**1. $\frac{1}{40} x_1 + \frac{1}{60} x_2 \leq 1$2. \(\frac{1}{5

dual of the given lppmin z=y1+y2s.t. 140y1+150y2≥3 160y1+150y2≥2 y1,y2≥0

Answered: max z = 3x, + 2x2 1 1 X1 + 40 X2 < 1 60…

Math

Advanced Math

max z = 3x, + 2x2 1 1 X1 + 40 X2 < 1 60 s.t. 1 X1 + 50 1 X2 < 1 50 X1, X2 20

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: Set up or formulate but do not solve the following LP problem. Be sure to include a well written…

A: Let x be the number of acres of wheat and y be the number of acres of barley to be planted. Given:…

Q: (c) TLF Ltd wishes to sell 28,000 units of its product, which has a variable cost of £30 to make and…

A: Add the fixed costs and target profit to get the should be contribution margin.Should be…

Q: (c) A jacket and two pairs of pants together cost $175. The jacket is valued at three times the…

A: Solution :-

Q: Tyler decided to open a bakery because everyone he knew told him that his baked goods were “out of…

Q: The demand for your college newspaper is 1800 copies per week if the paper is given a way free of…

A: The demand for your college newspaper is 1800 copies per week if the paper is given away free of…

Q: Suppose you're making hand-carved birdhouses to sell in an online store. The price function for how…

Q: suppose it costs $52,000 per year to live in city A. It costs $90,000 to live in city B. In which…

A: We have to find correct answer.

Q: The demand for your college newspaper is 1800 copies per week if the paper is given a way free of…

A: Given: Demand when charge is 0=1800 copies per week, Demand when charge is $0.10=900 copies per…

Q: C.W. Churchman once said that "Mathematics...tends to lull the unsuspecting that he who thinks…

A: No. Normally the best models of quantitative analysis are not mathematically complex. The reason is…

Q: The efficacy of two kinds of cognitive-behavioral therapy (CBT) in relation to a clinical population…

A: Tr A Tr B Mean 42.9 Mean 51.65 Standard Error 3.972206 Standard Error 4.0880…

Q: u very much! This question was super tricky.

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The cost of attending your university/college has once again gone up. One of the administrators at…

A: Given:

Q: A sandwich store rents space for $854 per month and wages amount to $1906 per month. Variable costs…

Q: d. At a country fair, adults' tickets sold for 5.50, senior citizens'sold for 4.00, and children's…

Q: 1) Look at page 204 in the textbook for a discussion of Profit. The calculation of Profit in a…

Q: Suppose we have the following supply and demand equation for a one pound bag of Snoopy’s Organic Dog…

A: The price of the one bag is given as $ 13.25.

Q: An audio company sells microphones for $110 per unit. Its fixed costs are $152,000 per year, and the…

A: Break even volume explain the minimum number of sales require to make the profit. It is calculated…

Q: A small business woman has realized that for one of her products, if the price per unit is GH&20 she…

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: The given revenue function Rx=60x-0.1x2 and the cost function Cx=6x+30. We have to find the maximum…

Q: Consider a manufacturing firm that has revenues of $160 per day. The firm must transport its output…

A: a) To find the firm's maximum willingness to pay per hectare of land at the central freight terminal…

Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

I just need the dual of the problem and an economic interpretation of it

### Linear Programming Problem

**Objective Function:**
\[ \text{max } z = 3x_1 + 2x_2 \]

**Subject to Constraints:**
1. $\frac{1}{40} x_1 + \frac{1}{60} x_2 \leq 1$
2. $\frac{1}{50} x_1 + \frac{1}{50} x_2 \leq 1$

**Non-negativity Constraints:**
\[ x_1, x_2 \geq 0 \]

**Task:**
Find the dual of this example and provide an economic interpretation of the problem.

This linear programming problem seeks to maximize the objective function $z$, subject to the given constraints. The variables $x_1$ and $x_2$ must be non-negative. The constraints represent limitations, such as resource or capacity restrictions, and the objective function represents a measure of profit or utility to be maximized. Finding the dual will offer insights into resource valuation and trade-offs.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Propositional Calculus$

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

PROBLEM OF THE WEEK Someone is opening their own funeral home business. They know that money will be tight, but they want to try to earn and income of $40,000 a year (for themselves) for the first year. The business owner takes out a loan to buy a building and equipment. The loan is expected to cost $900 a month The payments on a used hearse are estimated to be $200 per month. The lead car is estimated to be $150 per month. After some research, the insurance for the business is estimated to cost $1,500 per year Licensing/certification cost for the year: $250 Total estimated income from funerals: $110,000 The business owner will have three employees. They estimate that each employee will work 20 hours a week for each week of the year Income - expenses - 40,000 = x*employee hours
6. (a) A man has $4.55 in change composed entirely of dimes and quarters. What are the maximum and minimum number of coins that he can have? Is it possible for the number of dimes to equal the number of quarters? (b) The neighborhood theater charges $1.80 for adult admissions and $.75 for children. On a particular evening the total receipts were $90. Assuming that more adults than children were present, how many people attended? (c) A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum is 114. How many of each were there originally?
A small plant manufactures riding lawn mowers. The plant has a net fixed cost (leases, insurance, and so on) of$56000/day and variable costs (labor, materials, and so on) of $1600 per unit produced. The mowers are sold for $2000each unit per day. Write down the appropriate cost and revenue equations for the problem respectively. Using theseequations, answer the following questions:(a) How many units must be manufactured and sold each day for the company to maintain break-even trade?(b) Plot both equations simultaneously in a graph, and clearly indicate break-even point, equilibrium point andequilibrium price in this trade to maintain revenue as expected. Interpret the significance of the regions to the left- andright-side of the break-even point in this business.
Mr. Tran has $27,000 to invest, some in bonds and the rest in stocks. He has decided that the money invested in bonds must be at least twice as much as that in stocks. But the money invested in bonds must not be greater than $19,200. If the bonds earn 5%, and the stocks earn 8%, how much money should he invest in each to maximize his interest earned??
The new city water company that you have researched charges homeowners based on how much water they use in thousands of gallons. The company progressively charges at a higher rate the more water that is used. Cost of Water Bill (dollars) 240 230 220 210 190 180 170 160 110 Water Usage (in thousands of gallons) 11. Based on the graph above, how much does the city charge when a homeowner uses the following number of gallons of water: a) 1700 gallons of water b) 2000 gallons of water c) 7000 gallons of water 12. Finish filling in the following piece-wise equation below that describes the chart based on the graph 50 if 0 < x <2 5x+50 y = if 6≤x≤8 30x 140