Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Expert Solution & Answer
Chapter 4.10, Problem 4P
Explanation of Solution
LINGO output
- LINGO is an optimization modelling language that enables user to create many constraints or objective function terms by typing one line.
- LINGO is used to solve both linear and nonlinear problems.
- It is a software tool which is designed efficiently for building and solving linear, nonlinear and integer optimization.
- The LINGO model consists of three parts which are objective function, variables and constraints.
- The objective function is a formula that describes what the model optimizes exactly.
- Variables are the quantities that can be changed for producing the optimal value of the objective function.
- The constraint is the formula that defines the limits on the values of the variables.
- Here in the case of product matrix problem
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The Pee Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings
for electronic consumer products. All four presses operate differently and are of different sizes.
Currently the firm has a contract to produce three products. The contract calls for 400 units of product
1; 570 units of product 2; and 320 units of product 3. The time (in minutes) required for each product
to be produced on each machine is as follows: SOLVE THE MODEL BY USING MS EXCEL
At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…
A construction company has four large bulldozers located at four
different garages. The bulldozers are to be moved to four different construction
sites. The distances in miles between the bulldozers and the construction sites
are given below.
Bulldozer/
A
B
C
D
Site
Students
1
90
75
75
80
solve it
2
35
85
55
65
yourself
3
125
95
90
105
4
45
110
95
115
How should the bulldozers be moved to the construction sites in order to
minimize the total distance traveled?
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
- 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_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…arrow_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.arrow_forward
- Problem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a montharrow_forwardQuestion: Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. The gossip problem asks for G(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. a). Find G(1), G(2), G(3), and G(4). b). Use mathematical induction to prove that G(n) 4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.] c). Prove that G(n)= 2n – 4 for n> 4.arrow_forwardLet = 1.8-1 + 30 be a linear DDS. a) Suppose the initial value is = 59. Find the explicit solution. In b) Calculate the equilibrium value for this DDS. Round to 2 decimal places as needed. Ie c) Determine the stability of the equilibrium. Choose the correct answer. The equilibrium of this system is Select an answer because the slope is negative. the slope in absolute value is greater than 1. the slope is positive. the slope in absolute value is less than 1.arrow_forward
- 5. Consider the problem of predicting how well a student does in her second year of college/university, given how well she did in her first year. Specifically, let x be equal to the number of "A" grades (including A-. A and A+ grades) that a student receives in their first year of college (freshmen year). We would like to predict the value of y, which we define as the number of "A" grades they get in their second year (sophomore year). Here each row is one training example. Recall that in linear regression, our hypothesis is he(x)=0o+O;x, and we use m to denote the number of training examples. y 4 3 4 1 4 3 For the training set given above, what is the value of m? (which should be a number between 0 and 10).arrow_forwardYou are an investor who receives daily price quotes for a stock. The span of a stock's price on a given day is the number of consecutive days, from the given day going backwards, on which its price was less than or equal to its price on the day we are considering. Thus, the Stock Span Problem is as follows: Given a series of daily price quotes for a stock, find the span of the stock on each day of the series. Assume you are given seven daily stock quotes: 3, 10, 4, 7, 9, 6, and 8. Assume further that these stock quotes are stored in the array quotes. Show a step-by-step, manual desk-check execution of the algorithm below showing the values of all variables and arrays for each step in each cycle of each loop, as demonstrated in clase Algorithm: A Simple Stock Span Algorithm SimpleStockSpan (quotes) → spans Input: quotes, an array with n stock price quotes Output: spans, an array with n stock price spans 2 3 4 5 6 7 8 10 11 spans CreateArray (n) ← for i0 to n do k 1 span_end FALSE while…arrow_forwardYou are an investor who receives daily price quotes for a stock. The span of a stock's price on a given day is the number of consecutive days, from the given day going backwards, on which its price was less than or equal to its price on the day we are considering. Thus, the Stock Span Problem is as follows: Given a series of daily price quotes for a stock, find the span of the stock on each day of the series. Assume you are given seven daily stock quotes: 3, 10, 4, 7, 9, 6, and 8. Assume further that these stock quotes are stored in the array quotes. Show a step-by-step, manual desk-check execution of the algorithm below showing the values of all variables and arrays for each step in each cycle of each loop, as demonstrated in clase Algorithm: A Simple Stock Span Algorithm SimpleStockSpan (quotes) spans Input: quotes, an array with n stock price quotes Output: spans, an array with n stock price spans 1 spans CreateArray (n) 2 for i-0 to n do k+1 span_endFALSE while i-k 20 and not…arrow_forward
- 2. A whisky distiller named Taketsuru Masataka puts 8000L of whisky into barrels for aging, with 200L of whisky per barrel. Each year the volume of whisky in each barrel reduces by 2% due to evaporation (this is known as the angels' share). For the first 11 years after barreling, Taketsuru sells 2 barrels for 20 dollars per litre at the end of each year. Write bn for for the volume of whisky in each barrel at the beginning of year n, write Un for the total volume of whisky in storage at the beginning of year n, and rn for the total revenue from selling whisky at the beginning of year n. (a) Find a direct formula for bn. (b) Calculate the values of v₁, v2, V3 and then find a recursive definition for Un. (c) Find a recursive definition for rn. (d) Write a MATLAB program to compute Un and rn for n = 1, 2 ... 12 and display the values in three columns n, rn, Un with appropriate headings. (e) At the end of the 12th year Taketsuru finds that he can sell 12-year old whisky at the higher price…arrow_forward.An appliance manufacturer produces 2 models of microwave ovens: H and W. Both models require fabrication and assembly work; each H uses 4 hours of fabrication and 2 hours of assembly, and each W uses 2 hours of fabrication and 6 hours of assembly. There are 600 fabrication hours available this week and 480 hours of assembly. Each H contributes $40 towards profit, and each W contributes $30 towards profit. Use Linear Programming to find quantities of H and W that will maximize the profit. What is themaximum profit Please explain by excelarrow_forwardamyo Manufacturing produces four parts that require the use of a lathe and a drillpress. The two machines operate 10 hours a day. The following table provides the time inminutes required by each part:It is desired to balance the two machines by limiting thedifference between their total operation times to at most 30 minutes. The market demand for each part is at least 10 units. Additionally, the number of units of part 1 may not exceed that of part 2. b)Solve the following problems by B&B:Maximize ?=18?1+14?2+8?3+4?4subject to15?1+12?2+7?3+4?4+?5≤37?1,?2,?3,?4,?5=(0,1) Part 6arrow_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