Consider the following network representation of a transportation problem: Des Moines 25 14 Jefferson 30 City Kansas City 15 10 20 Omaha St. Louis 10 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. a. Develop a linear programming model for this problem; be sure to define the variables in your model. þ. Solve the linear program to determine the optimal solution.

Consider the following network representation of a transportation problem: Des Moines 25 14 Jefferson 30 City Kansas City 15 10 20 Omaha St. Louis 10 Supplies Demands The supplies, demands, and transportation costs per unit are shown on the network. a. Develop a linear programming model for this problem; be sure to define the variables in your model. þ. Solve the linear program to determine the optimal solution.

Name: 4.Consider the following network representation of a transportationpr
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: 4.Consider the following network representation of a transportationproblem:Des Moines2514Jefferson30CityKansasofCity151020OmahaSt. Louis10SuppliesDemandsThe supplies, demands, and transportation costs per unit are shown on thenetwork. a. Develop a l

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

Similar questions

4. Suppose the cost function for machine A has the following characteristics: a. it is linear, b. when the machine is not producing parts the cost is $200, c. cost of producing each part is $4 (i.e., variable cost is $4 per part). Suppose the cost function for machine B has the following characteristics: a. it is linear, b. when the machine is not producing parts the cost is $270, c. cost of producing each part is $3 (i.e., variable cost is $3 per part). A. Find the cost equations for machine A; place in function form. Define your variables B. Find the cost equations for machine B; place in function form. Define your variables (use variables that are different than variables used in Part A) C. Determine the break even point. (Determine this algebraically, not graphically; be sure to show your work.) D. Provide a graph of these two cost functions. Label the 1. Axes, 2. Break even point as an ordered pair, and 3. The two functions. E. To minimize cost, what production…
1. Maximization Model. Answer in complete solution.
A) The ABC engineering organization is supposed to carry out 5 types of repairs through five different operations. The table below gives the time required per each repair, the daily repair capacity of the operations and the profit gained per each repair.Formulate the problem as a linear programming model to maximize the profit. Operation Time per repair(minute) time Operations min/day F G H I J A 20 10 12 30 18 400 В 30 28 11 13 410 C 15 19 24 26 420 D 27 13 37 14 430 E 30 29 27 17 20 415 Profit 20 19 21 18 17 /repair
Formulate but do not solve the following exercise as a linear programming problem.A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3 on each unit of Product A and $5 on each unit of Product B. To manufacture a unit of Product A requires 5 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 5 min on Machine II. There are 269 min available on Machine I and 205 min available on Machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P in dollars? Maximize P = subject to the constraints Machine I Machine II x ≥ 0 y ≥ 0
1. Set up a linear programming model of the situation described. Determine whether it is in standard form. If not make it standard. A restaurant chef is planning a meal consisting of two foods, A, and B. • Each kg of A contains 3 units of fat and 6 units of protein • Each kg of B contains 1 unit of fat and 3 units of protein The chef wants the meal to consist of at least 18 units of protein and at most 6 units of fat. If the profit that he makes is 3 dollars per kg for food A and 5 dollars for food B, how many kilograms of each food should be served so as to maximize his profit?
Formulate but do not solve the following exercise as a linear programming problem. A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. She has decided that the meals are to be prepared from Foods A and B and that the meals should contain a minimum of 390 mg of calcium, 10 mg of iron, and 40 mg of vitamin C. Each ounce of Food A contains 25 mg of calcium, 2.5 mg of iron, 2 mg of vitamin C, and 6 mg of cholesterol. Each ounce of Food B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol. How many ounces of each type of food should be used in a meal so that the cholesterol content C (in mg) is minimized and the minimum requirements of calcium, iron, and vitamin C are met? Minimize C = subject to the constraints calcium iron vitamin C x ≥ 0 y ≥ 0
A linear programming computer package is needed. The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. Constraint Audience per advertisement Cost per advertisement Maximum media usage Radio Online Television Radio 300,000 54,000 120,000 $600 $2,000 10 $300 Online 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. (a) If the promotional budget is limited to $25,100, how many commercial messages should be run on each medium to maximize total audience contact? Television What is the allocation of the budget among the three media, and what is the…
Formulate a linear programming problem that can be used to solve the following question. A firm has plants in Boston and Baltimore that manufacture three models of hot tubs: regular, fancy, and super. In one day the Boston plant can manufacture 44 of the regular model, 32 of the fancy model, and 20 of the super model, and costs $4500 per day to operate, whereas the Baltimore plant can manufacture 12 of the regular model, 16 of the fancy model, and 58 of the super model, and costs $2000 per day to operate. At least 300 of the regular model, 320 of the fancy model, and 680 of the super model are needed. How many days must each plant operate in order to minimize the cost? ---1pəjəs-- = X y = ---Select--- ---Select--- v F = (objective function) Subject to (regular models) (fancy models) (super models) 0A---1pajas--
Set up the linear programming problem. Do not attempt to solve it. (See Example 1.) An import company obtains a license to import up to 180 pieces of hand-carved furniture. The importer may import chests, desks, and silverware boxes. The cost, volume, and profit are the following: Silverware Box Desk Chest $250 $160 $90 $320 $300 $50 7 12 1.5 The import company may purchase up to $4000 worth of furniture, and the furniture must all fit into a 1200-cubic-foot shipping container. Find the number of each type of furniture that should be ordered so that profit is maximum. (Let x₁ represent the number of chests, x₂ the number of acres of desks, x3 the number of silverware boxes, and z the profit in dollars.) ---Select--- V|Z = cost limitation Cost Profit Volume (cubic feet) space limitation maximum number allowed subject to X₁ ≥ 0, X₂ ≥ 0, X3 ≥ 0
The contribution to profits and overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2.- Formulate a linear programming model to determine how much of each type of pipe should be produced to maximize contribution to profits and to overhead, assuming that everything produced can be sold.- Find the optimal solution algebraically for the Moldex Company problem. What is the Z value when the decision variables have optimal values?