The three possible sources of energy to meet these needs are electricity, natural gas, and asolar heating unit that can be installed on the roof. The size of the roof limits the largestpossible solar heater to 30 units. Electricity can supply up to 20 units and natural gas cansupply up to 15 units . Electricity needs can be met only by purchasing electricity (at a costof $50 per unit). Both ather energy needs can be met by any source or combination ofsources. The unit cost areElectricityNatural GasSolar HeaterWater Heating$90$60$30Space Heating$80$50$40The objective is to minimize the total cost of meeting the energy needs.(a) Formulate this problem as a transportation problem by constructing the appropriateparameter table.(b) Use northwest corner rule to obtain the initial solution for this problem.(c) Starting with the initial solution, apply the stepping stone method to obtain the optimalsolution. 3. The Energetic Company needs to make plans for the energy systems for a new building.The energy needs in the building fall into three categories: (1) electricity, (2) heating water,and (3) heating space in the building. The daily requirements for these three categories (allmeasured in the same units) areThe three possible sources of energy to meet these needs are electricity, natural gas, and asolar heating unit that can be installed on the roof. The size of the roof limits the largestpossible solar heater to 30 units. Electricity can supply up to 20 units and natural gas cansupply up to 15 units . Electricity needs can be met only by purchasing electricity (at a costof $50 per unit). Both other energy needs can be met by any source or combination ofsources. The unit costs areElectricity20 unitsWater heating10 unitsSpace heating30 units

Given, Electricity- 20 units Water heating- 10 units Space Heating- 30 units

Answered: 3. The Energetic Company needs to make…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 84P

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The board of directors of General Wheels Company is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table. Investment Opportunity 1 2 3 4 5 6 7 Estimated Profit ($million) 17 10 15 19 7 13 9 Capital Required for Investment Opportunity ($million) Capital Available ($million) 1 2 3 4 5 6 7 Capital 43 28 34 48 17 32 23 100 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6, and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run…
DynaTune is trying to determine how to allocate its $145,000advertising budget for a new product. Radio and television arethe two media outlets selected for advertising. Th e followingtable shows the costs of advertising in these two media and theestimated number of new customers reached by increasingamounts of advertising For example, each of the fi rst 10 ads the company places on theradio will cost $1000 and is expected to reach 900 new customers.Each of the next 10 will cost $900 and is expected to reach 700new customers. Assume the company will purchase no more than30 radio ads and no more than 15 television ads.(a) Formulate an LP to maximize the number of newcustomers reached.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolution.(d) Suppose the number of new customers reached by 11–15television ads is 7500 and the number reached by 6–10ads is 5000. Resolve the problem. What is wrong with thissolution? Is Solver…
BIG produces four types of yogurts A, B, C, and D. Each box of yogurt carries protein, sugar, and Fat. The following table provides information about content of each box of yogurt together with production cost of each box. Protein /Box Sugar/Box Fat/Box Production Cost/Box Yogurt A 10 3 1.5 $ 2.00 Yogurt B 20 2 1 $ 3.00 Yogurt C 30 2.5 1.5 $ 5.00 Yogurt D 20 2 1.5 $ 3.50 BIG wants to produce yogurts in such a way that will provide at least 400 grams of protein with minimum production cost. However, BIG also have to make sure they are not providing more than 200 gm of Sugar and 200 gm of Fat while providing the required protein. Moreover, BIG has to produce at least one unit of each type of yogurt and the number of yogurt A produced should not be more than the number of yogurt C produced. SOLVE USING EXCEL SOLVER
You may produce seven products by consuming three materials. The unit sales price and material consumption of each product are listed in Table 1. For each day, the supply of these three materials are limited. The supply limits are listed in Table 2. For each day, you need to determine the production quantity for each product. Product Price Material 1 Material 2 Material 3 1 100 0 3 10 2 120 5 10 10 3 135 5 3 9 4 90 4 6 3 5 125 8 2 8 6 110 5 2 10 7 105 3 2 7 Table 1: Product information for Problem 1 Material Supply limit 1 100 2 150 3 200 Table 2: Material information for Problem 1 Formulate a linear integer program that generates a feasible production plan to maximize the total profit (which is also the total revenue, as there is no cost in this problem). Then write a computer program (e.g., using MS…
Mr Arda produces shampoo in the factory he owns. The shampoo he produces is unisex and reaches a wide target market. It only starts to produce products specific to women and men in line with the changing demands and needs. He creates a new product line for women, which includes eighteen different hair care products in this product line. These eighteen products fall into three separate categories. There are six products in each category. These categories consist of the aloe vera series, jasmine extract series, and coconut extract series. He wants to keep product prices slightly below the industry averages. It is known that the brand’s key competitors are Elidor and Dove.What price and distribution strategies should Mr. Arda use to compete with these brands? Explain with reasons
Mr. Barrera raises goats and pigs. He wants to raise no more than 16 animals including no more than 10 goats. It will cost $25 to raise each goat and $75 to raise each pig. She will make $12 in profit from each goat and $40 in profit from each pig. She has $900 to raise animals. How many of each type of animal should she raise to maximize profit?
1. Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. 2*x1 + x2 + x3 + x4 <= 2x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4s.t. x2 + x3 + x4 <= 2x1 + x2 <= 1x1 + x3 <= 1x1 + x4 <= 1x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1
ailco Corporation must determine how many sailboats should be produced during eachof the next four quarters (one quarter three months). The demand during each of thenext four quarters is as follows: first quarter, 40 sailboats; second quarter, 60 sailboats;third quarter, 75 sailboats; fourth quarter, 25 sailboats. Sailco must meet demands ontime. At the beginning of the first quarter, Sailco has an inventory of 10 sailboats. At thebeginning of each quarter, Sailco must decide how many sailboats should be producedduring that quarter. For simplicity, we assume that sailboats manufactured during a quarter can be used to meet demand for that quarter. During each quarter, Sailco can produceup to 40 sailboats with regular-time labor at a total cost of $400 per sailboat. By havingemployees work overtime during a quarter, Sailco can produce additional sailboats withovertime labor at a total cost of $450 per sailboat.At the end of each quarter (after production has occurred and the current…
1 ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops. Instructions: Develop a linear optimization model to determine how many of each type of desk the ABCD company should make next week to maximize profit contribution [Assume: S = units of standard desk produced and D = units of deluxe desk produced. No need to solve the model, neither graphically nor by Solver: just develop the mathematical model for this part].
Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following1) State the decision variables and constraints in this problem. 2) What is the objective function in this problem?…
Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following using the Solver application in Excel 4) Obtain a sensitivity report for the reported solution. Which constraints…
Case 2: A marketing research professor is conducting a telephone survey and needs to contact atleast 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 tomake a daytime call and $4 (because of higher labor costs) to make an evening call. The table shownbelow lists the expected results. For example, 10% of all daytime calls are answered by a single male,and 15% of all evening calls are answered by a single female. Because of a limited staff, at most halfof all phone calls can be evening calls. Determine how to minimize the cost of completing thesurvey. Percentages Daytime Evening Wife 25% 25% Husband 15% 30% Single male 10% 25% Single female 15% 15% None 35% 5% Develop a Report for the following using the Solver application on Excel 1) State the decision variables and constraints in this problem. 2) What is…

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