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Advanced Engineering Mathematics

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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"The set of points satisfying both the problem constraints and the nonnegative constraints in a linear programming problem is called the [Select] region for the problem."

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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 32 of the regular model, 24 of the fancy model, and 12 of the super model, and costs $2500 per day to operate, whereas the Baltimore plant can manufacture 12 of the regular model, 16 of the fancy model, and 31 of the super model, and costs $2500 per day to operate. At least 312 of the regular model, 360 of the fancy model, and 456 of the super model are needed. How many days must each plant operate in order to minimize the cost? x = ---Select--- y = ---Select--- ---Select--- ✓| F= Subject to X --Select--- 0, y ---Select--- 0 (objective function) (regular models) (fancy models) (super models)
Need only a handwritten solution only (not a typed one).
A linear programming problem is one that is concerned with finding the [Select] of a linear [Select] z = ax + by, where a and b do not both equal zero, and the [Select] variables and y are subject to the [Select] in the form of linear inequalities and equations. In addition, they must satisfy the nonnegative constraints of a > 0 and y ≥ 0. z of the form
The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as. The __________ assumption necessary for a linear programming model to be appropriate means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable. In problem formulation, the a. nonnegativity constraints are always ignored. b. optimal solution is decided upon. c. objective is expressed in terms of the decision variables. d. constraints are expressed in terms of the obtained objective function coefficients. Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem?
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?
The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0–1 integer linear programming model has been developed to determine which of the three machines (lathe, x1, press, x2, or grinder, x3) should be purchased in order to maximize annual profit: Maximize Z = 1000x1 + 700x2 + 800x3 (profit, $) subject to: $5,000x1 + 6,000x2 + 4,000x3 ≤ 10,000 (cost, $) x1 , x2 , x3 = 0 or 1 1. Solve this model by using the computer.

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