Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4.8, Problem 1P
Program Plan Intro
Given Linear
min z = -2x2
s.t x1 - x2 <= 4
-x1 + x2 <= 1
x1, x2>=0
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
2. Find all values of x that satisfy both inequalities simultaneously for
10x – 7> 17 and 2x + 3 < 11.
|
- The bucket has a weight of 400 N and is being hoisted
using three springs, each having an unstretched length of
6 = 0.45 m and stiffness of k = 800 N/m. Determine the
vertical distance d from the rim to point A for equilibrium.
400 N
D.
120
120°
0.45 m
120°
B
3d
EF, = 0; 400 –
F = 0
d² + (0.45)²
400 N
3d
[800 Jd² + (0.45)² -0.45)] = 0
400
d² + (4.5)²
|d² + (0.45)² -0.45) = 0.16667
0.45 m
d² + (4.5)²
d d² + (0.45)² -0.45 d = 0.16667 Jd² + (0.45)²
Va? + (0.45)² (d– 0.16667) = 0.45
0.45 m
d
[d² + (0.45)*] [d° – 2d(0.16667) + (0.16667)°] = (0.45)² d²
d* – 0.33334 d + 0.027779 d – 0.0675 d + 0.0056252 = 0
120°
0.45 m
d = 0.502 m
Ans
Q5/ A beam with a length L is attached to the wall with a cable as shown.
A load W = 400 lb.
is attached to the beam. The tension force, T,
in the cable is given by: T=!
WL√/h²+x²
hx
For a beam with L = 120 in and h=50 in
calculate T for x = 10, 30, 50, 70, 90, and 110 in.
Chapter 4 Solutions
Introduction to mathematical programming
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- You wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.arrow_forwardA motorist found that the efficiency of her engine could be increased by adding lubricatingoil to fuel. She experimented with different amounts of lubricating oil and the data areAmount of lubricating oil (ml) 0 25 50 75 100 Efficiency (%) 60 70 75 81 84(a) (10 points) Obtain the least squares fit of a straight line to the amount of lubricatingoil.(b) (10 points) Test whether or not the slope β1 = 0. Take α = 0.05 as your level ofsignificance.(c) (10 points) Construct a 90% confidence interval on the mean response at x0 = 10 ml.(d) (10 points) Give a point estimate of the mean engine efficiency when the amount oflubricating oil is 450 ml.(e) (10 points) What additional danger is there when using your estimate in part (d)?arrow_forwardGiven the following function: f(x) = 2x For g(x) = Sf(x) dx, determine g(x).arrow_forward
- Consider the titration of 100.0 mL of 0.200 M acetic acid (K₂ = 1.8 × 10-5) by 0.100 M KOH. Calculate the pH of the resulting solution after the following volumes of KOH have been added. a. 0.0 mL pH = b. 50.0 mL pH = c. 100.0 mL pH = d. 150.0 mL pH = e. 200.0 mL pH = f. 210.0 mL pH =arrow_forwardShow that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.arrow_forwardCurrent Attempt in Progress The accompanying figure shows known flow rates of hydrocarbons into and out of a network of pipes at an oil refinery. 200 E X3 D 150 X5 X₁' 200 25 A B x2 175 C (a) Set up a linear system whose solution provides the unknown flow rates. 25 X2 175 X3 Find A so that Ax=y where = and y = 200 THO 150 200 Form the system so that the first equation represents node A, the second equation node B, etc. Then take all the variable to one side such that all the constants are on one side and positive. From the equations form the required matrices and enter the appropriate values for A below. A =arrow_forward
- At the beginning of the first day (day 1) after grape harvesting is completed, a grapegrower has 8000 kg of grapes in storage. At the end of day n, for n = 1, 2, . . . , the grape grower sells 250n/(n + 1) kg of their stored grapes at the local market at the price of $1.50 per kg.During each day the stored grapes dry out a little so that their weight decreases by 2%.Let wn be the weight (in kg) of the stored grapes at the beginning of day n for n ≥ 1.Find a recursive definition for wn. Draw a timeline. Find the value of wn for n = 1, 2, 3. Let rn be the total revenue (in dollars) earned from the stored grapes from the beginning of day 1 up to the beginning of day n for n ≥ 1.Write a program to compute wn and rn for n = 1, 2, . . . , num where num is entered by the user, and display the values in three columns: n, wn, rn with appropriate headings.Run the program for num = 20. (Use format bank.) Use program to determine how many days it will take to sell all of the grapes.//This is all…arrow_forwardc) Knowing that we have the equality: 12Ar+3= B2hez determine the value of x and encircle it.arrow_forwardQuestion 4 A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested inthe probability that the number appearing on the blue die is less than that appearing on theyellow die which is less than that appearing on the red die. (That is, if B (R) [Y ] is the numberappearing on the blue (red) [yellow] die, then we are interested in P(B < Y < R). )(a) What is the probability that no two of the dice land on the same number?(b) Given that no two of the dice land on the same number, what is theconditional probability that B < Y < R?(c) What is P(B < Y < R)?arrow_forward
- [7] Simplify the following Boolean function F, together with the don't-care conditions d, and then express the simplified function in sum-of-minterms form: (d) F(A, B, C, D) = E(1,3,8, 10, 15) and d(A,B,C,D) = E(0, 2,9) IUW Y .. [9] Simplify the following functions, and implement them with two-level NOR gate circuits: (b) F(w,x,y, z) = E(1,2, 13, 14) [10] (a) Implement the following function using NAND gates with a fan in of 2. F = (ab + d') (ac + b) + (ac +b)d (b) Simplify the above function and implement using NAND gates with a fan in of 2. [11] Determine the value of F in a standard form: y Z' F y'arrow_forwardTheorem 1 (Master Theorem). Let a ≥ 1 and b> 1 be constants, let f(n) be a function f: N→ R+, and let T(n) be defined on the nonnegative integers by the recurrence T(n)= aT(n/b) + f(n). Then T(n) has the following asymptotic bounds: 1. if f(n) = O(nlogs a-E) for some constant e > 0, then T(n) = (nossa), 2. if f(n) = (nlos a) then T(n) = (nloga log n), and 3. if f(n) = N(n¹og a+s) for some e > 0 and if af (n/b) ≤df (n) for some constant d < 1 and all sufficiently large n, then T(n) = (f(n)). Use the Master Theorem above to solve the following recurrences when possible (note that not every blank needs to be filled in in every problem):arrow_forwardSolution plz..arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole